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@sebastiendesignolle
sebastiendesignolle committed Feb 8, 2023
1 parent cd97eab commit 25cabb2
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Showing 4 changed files with 92 additions and 83 deletions.
4 changes: 2 additions & 2 deletions examples/CHSH.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -10,10 +10,10 @@ measurements_vecA = [1 0 0; 0 0 1]
measurements_vecB = [1 0 1; 1 0 -1] / sqrt(2)
rho = rho_singlet() # shared state
_, lower_bound, upper_bound, local_model, bell_inequality, _ =
nonlocality_threshold([measurements_vecA, measurements_vecB], N; rho = rho)
nonlocality_threshold([measurements_vecA, measurements_vecB], N; rho=rho)

println("Correlation matrix")
p = correlation_tensor([measurements_vecA, measurements_vecB], N; rho = rho, marg = false)
p = correlation_tensor([measurements_vecA, measurements_vecB], N; rho=rho, marg=false)
display(p)

println()
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4 changes: 2 additions & 2 deletions examples/GHZ.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -8,10 +8,10 @@ N = 3 # tripartite scenario
measurements_vec = polygonXY_vec(8)
rho = rho_GHZ(N) # shared state
lower_bound_infinite, lower_bound, upper_bound, local_model, bell_inequality, _ =
nonlocality_threshold(measurements_vec, N; rho = rho) # the marginals vanish in this case
nonlocality_threshold(measurements_vec, N; rho=rho) # the marginals vanish in this case

println("Correlation tensor")
p = correlation_tensor(measurements_vec, N; rho = rho, marg = false)
p = correlation_tensor(measurements_vec, N; rho=rho, marg=false)
display(p[:, :, 1]) # only printing part of the tensor

println()
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14 changes: 7 additions & 7 deletions examples/Werner.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -9,15 +9,15 @@ N = 2 # bipartite scenario
# obtained with https://github.com/sebastiendesignolle/polyhedronisme
measurements_vec = polyhedronisme("../polyhedra/polyhedronisme-SASuSAuO.obj", 33)
rho = rho_singlet() # shared state
p = correlation_tensor(measurements_vec, N; rho = rho, marg = false)
p = correlation_tensor(measurements_vec, N; rho=rho, marg=false)
x, ds, primal, dual_gap, traj_data, as, M, β = bell_frank_wolfe(
p;
v0 = 1 / sqrt(2),
verbose = 3,
epsilon = 1e-4,
lazy_tolerance = 0.5,
mode_last = 0,
nb_last = 10^6,
v0=1 / sqrt(2),
verbose=3,
epsilon=1e-4,
lazy_tolerance=0.5,
mode_last=0,
nb_last=10^6,
)
# v_c ≤ 0.704826 (heuristic local bound)

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153 changes: 81 additions & 72 deletions src/BellPolytopes.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -55,33 +55,33 @@ Optional arguments:
"""
function bell_frank_wolfe(
p::Array{T,N};
marg::Bool = N == 2 ? false : true,
v0 = one(T),
epsilon = 1e-7,
verbose = 0,
shr2 = NaN,
TD::DataType = T,
mode::Int = 0,
nb::Int = 10^2,
TL::DataType = T,
mode_last::Int = 0,
nb_last::Int = 10^5,
sym::Union{Nothing,Bool} = nothing,
use_array::Union{Nothing,Bool} = nothing,
active_set = nothing, # warm start
lazy::Bool = true, # default in FW package is false
max_iteration::Int = 10^7, # default in FW package is 10^4
recompute_last_vertex = false, # default in FW package is true
callback_interval::Int = verbose > 0 ? 10^4 : typemax(Int),
renorm_interval::Int = verbose > 0 ? callback_interval : typemax(Int),
reduce_interval::Int = verbose > 0 ? 100callback_interval : typemax(Int),
hyperplane_interval::Int = verbose > 0 ? 10callback_interval : typemax(Int),
bound_interval::Int = verbose > 0 ? 10callback_interval : typemax(Int),
nb_increment_interval::Int = verbose > 0 ? 10callback_interval : typemax(Int),
save_interval::Int = verbose > 0 ? 100callback_interval : typemax(Int),
save::Bool = false,
file = nothing,
seed::Int = 0,
marg::Bool=N == 2 ? false : true,
v0=one(T),
epsilon=1e-7,
verbose=0,
shr2=NaN,
TD::DataType=T,
mode::Int=0,
nb::Int=10^2,
TL::DataType=T,
mode_last::Int=0,
nb_last::Int=10^5,
sym::Union{Nothing,Bool}=nothing,
use_array::Union{Nothing,Bool}=nothing,
active_set=nothing, # warm start
lazy::Bool=true, # default in FW package is false
max_iteration::Int=10^7, # default in FW package is 10^4
recompute_last_vertex=false, # default in FW package is true
callback_interval::Int=verbose > 0 ? 10^4 : typemax(Int),
renorm_interval::Int=verbose > 0 ? callback_interval : typemax(Int),
reduce_interval::Int=verbose > 0 ? 100callback_interval : typemax(Int),
hyperplane_interval::Int=verbose > 0 ? 10callback_interval : typemax(Int),
bound_interval::Int=verbose > 0 ? 10callback_interval : typemax(Int),
nb_increment_interval::Int=verbose > 0 ? 10callback_interval : typemax(Int),
save_interval::Int=verbose > 0 ? 100callback_interval : typemax(Int),
save::Bool=false,
file=nothing,
seed::Int=0,
kwargs...,
) where {T<:Number} where {N}
Random.seed!(seed)
Expand Down Expand Up @@ -127,12 +127,12 @@ function bell_frank_wolfe(
# create the LMO
lmo = BellCorrelationsLMO(
vp;
mode = mode,
nb = nb,
sym = sym,
marg = marg,
use_array = use_array,
reynolds = reynolds,
mode=mode,
nb=nb,
sym=sym,
marg=marg,
use_array=use_array,
reynolds=reynolds,
)
# useful to make f efficient
normp2 = dot(vp, vp) / 2
Expand All @@ -155,11 +155,11 @@ function bell_frank_wolfe(
if active_set isa ActiveSetStorage
active_set = load_active_set(
active_set;
type = TD,
sym = sym,
marg = marg,
use_array = use_array,
reynolds = reynolds,
type=TD,
sym=sym,
marg=marg,
use_array=use_array,
reynolds=reynolds,
)
end
active_set_link_lmo!(active_set, lmo)
Expand Down Expand Up @@ -196,15 +196,15 @@ function bell_frank_wolfe(
grad!,
lmo,
active_set;
callback = callback,
epsilon = epsilon,
lazy = lazy,
line_search = FrankWolfe.Shortstep(one(TD)),
max_iteration = max_iteration,
recompute_last_vertex = recompute_last_vertex,
renorm_interval = typemax(Int),
trajectory = true,
verbose = false,
callback=callback,
epsilon=epsilon,
lazy=lazy,
line_search=FrankWolfe.Shortstep(one(TD)),
max_iteration=max_iteration,
recompute_last_vertex=recompute_last_vertex,
renorm_interval=typemax(Int),
trajectory=true,
verbose=false,
kwargs...,
)
if verbose ≥ 2
Expand All @@ -215,7 +215,7 @@ function bell_frank_wolfe(
@printf(" It/sec: %.2e\n", traj_data[end][1] / traj_data[end][5])
@printf(" #Atoms: %d\n", length(as))
end
atoms = BellCorrelationsDS.(as.atoms; type = TL)
atoms = BellCorrelationsDS.(as.atoms; type=TL)
as = FrankWolfe.ActiveSet{eltype(atoms),TL,Array{TL,N}}(
TL.(as.weights),
atoms,
Expand All @@ -227,14 +227,14 @@ function bell_frank_wolfe(
if mode_last ≥ 0 # bypass the last LMO with a negative mode
time_start = time_ns()
ds = FrankWolfe.compute_extreme_point(
BellCorrelationsLMO(lmo; mode = mode_last, type = TL, nb = nb_last),
BellCorrelationsLMO(lmo; mode=mode_last, type=TL, nb=nb_last),
-M;
verbose = verbose > 0,
last = true,
verbose=verbose > 0,
last=true,
)
time = time_ns() - time_start
else
ds = BellCorrelationsDS(ds; type = TL)
ds = BellCorrelationsDS(ds; type=TL)
end
β = FrankWolfe.fast_dot(M, ds) # local/global max found by the LMO
dual_gap = FrankWolfe.fast_dot(x - vp, x) - FrankWolfe.fast_dot(x - vp, ds)
Expand All @@ -257,8 +257,17 @@ end
"""
Compute the local bound of a Bell inequality parametrised by `M`.
"""
function local_bound(M::Array{T, N}; mode::Int = 1, nb::Int = 10^5, verbose = false) where {T<:Number} where {N}
ds = FrankWolfe.compute_extreme_point(BellCorrelationsLMO(M; mode = mode, nb = nb), -M; verbose = verbose)
function local_bound(
M::Array{T,N};
mode::Int=1,
nb::Int=10^5,
verbose=false,
) where {T<:Number} where {N}
ds = FrankWolfe.compute_extreme_point(
BellCorrelationsLMO(M; mode=mode, nb=nb),
-M;
verbose=verbose,
)
return FrankWolfe.fast_dot(M, ds), ds
end

Expand All @@ -285,16 +294,16 @@ Optional arguments:
function nonlocality_threshold(
vec::Union{TB,Vector{TB}},
N::Int;
rho = N == 2 ? rho_singlet(; type = T) : rho_GHZ(N; type = T),
epsilon = 1e-8,
marg::Bool = false,
v0 = one(T),
precision = 4,
verbose = -1,
rho=N == 2 ? rho_singlet(; type=T) : rho_GHZ(N; type=T),
epsilon=1e-8,
marg::Bool=false,
v0=one(T),
precision=4,
verbose=-1,
kwargs...,
) where {TB<:AbstractMatrix{T}} where {T<:Number}
p = correlation_tensor(vec, N; rho = rho, marg = marg)
shr2 = shrinking_squared(vec; verbose = verbose > 0)
p = correlation_tensor(vec, N; rho=rho, marg=marg)
shr2 = shrinking_squared(vec; verbose=verbose > 0)
lower_bound = zero(T)
upper_bound = one(T)
local_model = nothing
Expand All @@ -303,11 +312,11 @@ function nonlocality_threshold(
while upper_bound - lower_bound > 10.0^(-precision)
res = bell_frank_wolfe(
p;
v0 = v0,
verbose = verbose + (upper_bound == one(T)) / 2,
epsilon = epsilon,
shr2 = shr2,
marg = marg,
v0=v0,
verbose=verbose + (upper_bound == one(T)) / 2,
epsilon=epsilon,
shr2=shr2,
marg=marg,
kwargs...,
)
push!(traj_data, res)
Expand All @@ -317,12 +326,12 @@ function nonlocality_threshold(
end
if dual_gap < primal
if β < upper_bound
upper_bound = round(β; digits = precision)
upper_bound = round(β; digits=precision)
bell_inequality = M
if v0 == round(β; digits = precision)
v0 = round(β - 10.0^(-precision); digits = precision)
if v0 == round(β; digits=precision)
v0 = round(β - 10.0^(-precision); digits=precision)
else
v0 = round(β; digits = precision)
v0 = round(β; digits=precision)
end
else
@warn "Unexpected output"
Expand All @@ -332,7 +341,7 @@ function nonlocality_threshold(
lower_bound = v0
local_model = as
if upper_bound < lower_bound
upper_bound = round(v0 + 2*10.0^(-precision); digits = precision)
upper_bound = round(v0 + 2 * 10.0^(-precision); digits=precision)
end
v0 = (lower_bound + upper_bound) / 2
end
Expand Down

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