kalmar/PropertyT.jl
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replace all shows and printlns by info(logger,...

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kalmar 2017-03-15 17:51:13 +01:00
parent 94389b887a
commit 02a89908db
3 changed files with 74 additions and 72 deletions
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57
src/PropertyT.jl
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@ -36,7 +36,7 @@ function ΔandSDPconstraints(name::String)
f₁ = isfile(pm_fname) f₁ = isfile(pm_fname)
f₂ = isfile(Δ_fname) f₂ = isfile(Δ_fname)
if f₁ && f₂ if f₁ && f₂
println("Loading precomputed pm, Δ, sdp_constraints...") info(logger, "Loading precomputed pm, Δ, sdp_constraints...")
product_matrix = load(pm_fname, "pm") product_matrix = load(pm_fname, "pm")
L = load(Δ_fname, "Δ")[:, 1] L = load(Δ_fname, "Δ")[:, 1]
Δ = GroupAlgebraElement(L, Array{Int,2}(product_matrix)) Δ = GroupAlgebraElement(L, Array{Int,2}(product_matrix))
@ -60,7 +60,7 @@ function κandA(name::String)
f₁ = isfile(κ_fname) f₁ = isfile(κ_fname)
f₂ = isfile(SDP_fname) f₂ = isfile(SDP_fname)
if f₁ && f₂ if f₁ && f₂
println("Loading precomputed κ, A...") info(logger, "Loading precomputed κ, A...")
κ = load(κ_fname, "κ") κ = load(κ_fname, "κ")
A = load(SDP_fname, "A") A = load(SDP_fname, "A")
else else
@ -79,9 +79,11 @@ function timed_msg(t)
end end
function κandA(name::String, sdp_constraints, Δ::GroupAlgebraElement, solver::AbstractMathProgSolver; upper_bound=Inf) function κandA(name::String, sdp_constraints, Δ::GroupAlgebraElement, solver::AbstractMathProgSolver; upper_bound=Inf)
println("Creating SDP problem...") info(logger, "Creating SDP problem...")
@time SDP_problem = create_SDP_problem(sdp_constraints, Δ; upper_bound=upper_bound) t = @timed SDP_problem = create_SDP_problem(sdp_constraints, Δ; upper_bound=upper_bound)
println("Solving SDP problem maximizing κ...") info(logger, timed_msg(t))
info(logger, "Solving SDP problem maximizing κ...")
κ, A = solve_SDP(SDP_problem, solver) κ, A = solve_SDP(SDP_problem, solver)
κ_fname, A_fname = κSDPfilenames(name) κ_fname, A_fname = κSDPfilenames(name)
if κ > 0 if κ > 0
@ -94,15 +96,19 @@ function κandA(name::String, sdp_constraints, Δ::GroupAlgebraElement, solver::
end end
function check_property_T(name::String, ID, generate_B₄::Function; function check_property_T(name::String, ID, generate_B₄::Function;
verbose=true, tol=1e-6, upper_bound=Inf) tol=1e-6, upper_bound=Inf)
# solver = MosekSolver(INTPNT_CO_TOL_REL_GAP=tol, QUIET=!verbose) if !isdir(name)
solver = SCSSolver(eps=tol, max_iters=100000, verbose=verbose) mkdir(name)
end
@show name add_handler(logger, DefaultHandler("./$name/full.log"), "full")
@show verbose add_handler(solver_logger, DefaultHandler("./$name/solver.log"), "solver")
@show tol info(logger, "Group: $name")
info(logger, "Precision: $tol")
# solver = MosekSolver(INTPNT_CO_TOL_REL_GAP=tol, QUIET=false)
solver = SCSSolver(eps=tol, max_iters=1000000, verbose=true)
Δ, sdp_constraints = try Δ, sdp_constraints = try
ΔandSDPconstraints(name) ΔandSDPconstraints(name)
@ -110,12 +116,13 @@ function check_property_T(name::String, ID, generate_B₄::Function;
if isa(err, ArgumentError) if isa(err, ArgumentError)
ΔandSDPconstraints(name, ID, generate_B₄) ΔandSDPconstraints(name, ID, generate_B₄)
else else
throw(err) error(logger, err)
end end
end end
println("|S| = $(countnz(Δ.coefficients) -1)")
@show length(Δ) info(logger, "|S| = $(countnz(Δ.coefficients) - 1)")
@show size(Δ.product_matrix) info(logger, "length(Δ) = $(length(Δ))")
info(logger, "size(Δ.product_matrix) = $(size(Δ.product_matrix))")
κ, A = try κ, A = try
κandA(name) κandA(name)
@ -123,26 +130,26 @@ function check_property_T(name::String, ID, generate_B₄::Function;
if isa(err, ArgumentError) if isa(err, ArgumentError)
κandA(name, sdp_constraints, Δ, solver; upper_bound=upper_bound) κandA(name, sdp_constraints, Δ, solver; upper_bound=upper_bound)
else else
throw(err) # throw(err)
error(logger, err)
end end
end end
@show κ info(logger, "κ = $κ")
@show sum(A) info(logger, "sum(A) = $(sum(A))")
@show maximum(A) info(logger, "maximum(A) = $(maximum(A))")
@show minimum(A) info(logger, "minimum(A) = $(minimum(A))")
if κ > 0 if κ > 0
true_kappa = check_distance_to_positive_cone(Δ, κ, A, tol=tol, rational=false)
true_kappa = check_distance_to_positive_cone(Δ, κ, A, tol=tol, verbose=verbose, rational=false)
true_kappa = Float64(trunc(true_kappa,12)) true_kappa = Float64(trunc(true_kappa,12))
if true_kappa > 0 if true_kappa > 0
println("κ($name, S) ≥ $true_kappa: Group HAS property (T)!") info(logger, "κ($name, S) ≥ $true_kappa: Group HAS property (T)!")
else else
println("κ($name, S) ≥ $true_kappa: Group may NOT HAVE property (T)!") info(logger, "κ($name, S) ≥ $true_kappa: Group may NOT HAVE property (T)!")
end end
else else
println("κ($name, S) ≥ $κ < 0: Tells us nothing about property (T)") info(logger, "κ($name, S) ≥ $κ < 0: Tells us nothing about property (T)")
end end
end end

77
src/checksolution.jl
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@ -61,99 +61,94 @@ end
ℚ(x, tol::Real) = rationalize(BigInt, x, tol=tol) ℚ(x, tol::Real) = rationalize(BigInt, x, tol=tol)
function distance_to_cone{T<:Rational}(κ::T, sqrt_matrix::Array{T,2}, Δ::GroupAlgebraElement{T}; verbose=true, augmented=false) function distance_to_cone{T<:Rational}(κ::T, sqrt_matrix::Array{T,2}, Δ::GroupAlgebraElement{T})
SOS = compute_SOS(sqrt_matrix, Δ) SOS = compute_SOS(sqrt_matrix, Δ)
if augmented
epsilon = GroupAlgebras.ɛ(SOS)
@show epsilon
end
SOS_diff = EOI(Δ, κ) - SOS SOS_diff = EOI(Δ, κ) - SOS
eoi_SOS_L₁_dist = norm(SOS_diff,1) eoi_SOS_L₁_dist = norm(SOS_diff,1)
if verbose info(logger, "κ = $κ")
@show κ
ɛ_dist = GroupAlgebras.ɛ(SOS_diff) ɛ_dist = GroupAlgebras.ɛ(SOS_diff)
L₁_dist = eoi_SOS_L₁_dist if ɛ_dist ≠ 0//1
@printf("ɛ(Δ² - κΔ - ∑ξᵢ*ξᵢ) = %.10f\n", float(ɛ_dist)) warn(logger, "The SOS is not in the augmentation ideal, number below are meaningless!")
@printf("‖Δ² - κΔ - ∑ξᵢ*ξᵢ‖₁ = %.10f\n", float(L₁_dist))
end end
info(logger, "ɛ(Δ² - κΔ - ∑ξᵢ*ξᵢ) = $ɛ_dist")
info(logger, "‖Δ² - κΔ - ∑ξᵢ*ξᵢ‖₁ = $(@sprintf("%.10f", float(eoi_SOS_L₁_dist)))")
distance_to_cone = κ - 2^3*eoi_SOS_L₁_dist distance_to_cone = κ - 2^3*eoi_SOS_L₁_dist
return distance_to_cone return distance_to_cone
end end
function distance_to_cone{T<:Rational, S<:Interval}(κ::T, sqrt_matrix::Array{S,2}, Δ::GroupAlgebraElement{T}; verbose=true) function distance_to_cone{T<:Rational, S<:Interval}(κ::T, sqrt_matrix::Array{S,2}, Δ::GroupAlgebraElement{T})
SOS = compute_SOS(sqrt_matrix, Δ) SOS = compute_SOS(sqrt_matrix, Δ)
verbose && println("ɛ(∑ξᵢ*ξᵢ) ∈ $(GroupAlgebras.ɛ(SOS))") info(logger, "ɛ(∑ξᵢ*ξᵢ) ∈ $(GroupAlgebras.ɛ(SOS))")
SOS_diff = EOI(Δ, κ) - SOS SOS_diff = EOI(Δ, κ) - SOS
eoi_SOS_L₁_dist = norm(SOS_diff,1) eoi_SOS_L₁_dist = norm(SOS_diff,1)
if verbose info(logger, "κ = $κ")
@show κ
ɛ_dist = GroupAlgebras.ɛ(SOS_diff) ɛ_dist = GroupAlgebras.ɛ(SOS_diff)
println("ɛ(Δ² - κΔ - ∑ξᵢ*ξᵢ) ∈ $(ɛ_dist)") info(logger, "ɛ(Δ² - κΔ - ∑ξᵢ*ξᵢ) ∈ $(ɛ_dist)")
println("‖Δ² - κΔ - ∑ξᵢ*ξᵢ‖₁ ∈ $(eoi_SOS_L₁_dist)") info(logger, "‖Δ² - κΔ - ∑ξᵢ*ξᵢ‖₁ ∈ $(eoi_SOS_L₁_dist)")
end
distance_to_cone = κ - 2^3*eoi_SOS_L₁_dist distance_to_cone = κ - 2^3*eoi_SOS_L₁_dist
return distance_to_cone return distance_to_cone
end end
function distance_to_cone{T<:AbstractFloat}(κ::T, sqrt_matrix::Array{T,2}, Δ::GroupAlgebraElement{T}; verbose=true) function distance_to_cone{T<:AbstractFloat}(κ::T, sqrt_matrix::Array{T,2}, Δ::GroupAlgebraElement{T})
SOS = compute_SOS(sqrt_matrix, Δ) SOS = compute_SOS(sqrt_matrix, Δ)
SOS_diff = EOI(Δ, κ) - SOS SOS_diff = EOI(Δ, κ) - SOS
eoi_SOS_L₁_dist = norm(SOS_diff,1) eoi_SOS_L₁_dist = norm(SOS_diff,1)
if verbose info(logger, "κ = $κ (≈$(float(κ)))")
println("κ = $κ (≈$(float(κ)))")
ɛ_dist = GroupAlgebras.ɛ(SOS_diff) ɛ_dist = GroupAlgebras.ɛ(SOS_diff)
@printf("ɛ(Δ² - κΔ - ∑ξᵢ*ξᵢ) ≈ %.10f\n", ɛ_dist) info(logger, "ɛ(Δ² - κΔ - ∑ξᵢ*ξᵢ) ≈ $(@sprintf("%.10f\n", ɛ_dist))")
@printf("‖Δ² - κΔ - ∑ξᵢ*ξᵢ‖₁ ≈ %.10f\n", eoi_SOS_L₁_dist) info(logger, "‖Δ² - κΔ - ∑ξᵢ*ξᵢ‖₁ ≈ $(@sprintf("%.10f\n", eoi_SOS_L₁_dist))")
end
distance_to_cone = κ - 2^3*eoi_SOS_L₁_dist distance_to_cone = κ - 2^3*eoi_SOS_L₁_dist
return distance_to_cone return distance_to_cone
end end
function check_distance_to_positive_cone(Δ::GroupAlgebraElement, κ, A; function check_distance_to_positive_cone(Δ::GroupAlgebraElement, κ, A;
tol=1e-7, verbose=true, rational=false) tol=1e-7, rational=false)
isapprox(eigvals(A), abs(eigvals(A)), atol=tol) || isapprox(eigvals(A), abs(eigvals(A)), atol=tol) ||
warn("The solution matrix doesn't seem to be positive definite!") warn("The solution matrix doesn't seem to be positive definite!")
@assert A == Symmetric(A) @assert A == Symmetric(A)
A_sqrt = real(sqrtm(A)) A_sqrt = real(sqrtm(A))
println("-------------------------------------------------------------") info(logger, "-------------------------------------------------------------")
println("") info(logger, "")
println("Checking in floating-point arithmetic...") info(logger, "Checking in floating-point arithmetic...")
@time fp_distance = distance_to_cone(κ, A_sqrt, Δ, verbose=verbose) @time fp_distance = distance_to_cone(κ, A_sqrt, Δ)
println("Floating point distance (to positive cone)\n ≈ $(Float64(trunc(fp_distance,10)))") info(logger, "Floating point distance (to positive cone)\n ≈ $(Float64(trunc(fp_distance,10)))")
println("-------------------------------------------------------------") info(logger, "-------------------------------------------------------------")
println("") info(logger, "")
println("Projecting columns of rationalized A_sqrt to the augmentation ideal...") info(logger, "Projecting columns of rationalized A_sqrt to the augmentation ideal...")
δ = eps(κ) δ = eps(κ)
A_sqrt_ℚ = ℚ(A_sqrt, δ) A_sqrt_ℚ = ℚ(A_sqrt, δ)
A_sqrt_ℚ_aug = correct_to_augmentation_ideal(A_sqrt_ℚ) A_sqrt_ℚ_aug = correct_to_augmentation_ideal(A_sqrt_ℚ)
κ_ℚ = ℚ(κ, δ) κ_ℚ = ℚ(κ, δ)
Δ_ℚ = ℚ(Δ, δ) Δ_ℚ = ℚ(Δ, δ)
println("Checking in interval arithmetic") info(logger, "Checking in interval arithmetic")
A_sqrt_ℚ_augᴵ = A_sqrt_ℚ_aug ± δ A_sqrt_ℚ_augᴵ = A_sqrt_ℚ_aug ± δ
@time Interval_dist_to_Σ² = distance_to_cone(κ_ℚ, A_sqrt_ℚ_augᴵ, Δ_ℚ, verbose=verbose) @time Interval_dist_to_Σ² = distance_to_cone(κ_ℚ, A_sqrt_ℚ_augᴵ, Δ_ℚ)
println("The Augmentation-projected actual distance (to positive cone) belongs to \n$Interval_dist_to_Σ²") info(logger, "The Augmentation-projected actual distance (to positive cone) belongs to \n$Interval_dist_to_Σ²")
println("-------------------------------------------------------------") info(logger, "-------------------------------------------------------------")
println("") info(logger, "")
if Interval_dist_to_Σ².lo ≤ 0 if Interval_dist_to_Σ².lo ≤ 0
return Interval_dist_to_Σ².lo return Interval_dist_to_Σ².lo
else else
println("Checking Projected SOS decomposition in exact rational arithmetic...") info(logger, "Checking Projected SOS decomposition in exact rational arithmetic...")
@time ℚ_dist_to_Σ² = distance_to_cone(κ_ℚ, A_sqrt_ℚ_aug, Δ_ℚ, verbose=verbose, augmented=true) @time ℚ_dist_to_Σ² = distance_to_cone(κ_ℚ, A_sqrt_ℚ_aug, Δ_ℚ, augmented=true)
@assert isa(ℚ_dist_to_Σ², Rational) @assert isa(ℚ_dist_to_Σ², Rational)
println("Augmentation-projected rational distance (to positive cone)\n ≥ $(Float64(trunc(ℚ_dist_to_Σ²,8)))") info(logger, "Augmentation-projected rational distance (to positive cone)\n ≥ $(Float64(trunc(ℚ_dist_to_Σ²,8)))")
println("-------------------------------------------------------------") info(logger, "-------------------------------------------------------------")
return ℚ_dist_to_Σ² return ℚ_dist_to_Σ²
end end
end end

6
src/sdps.jl
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@ -68,8 +68,8 @@ function create_SDP_problem(matrix_constraints, Δ::GroupAlgebraElement; upper_b
end end
function solve_SDP(SDP_problem, solver) function solve_SDP(SDP_problem, solver)
@show SDP_problem info(logger, Base.repr(m))
@show solver info(logger, solver)
JuMP.setsolver(SDP_problem, solver); JuMP.setsolver(SDP_problem, solver);
# @time MathProgBase.writeproblem(SDP_problem, "/tmp/SDP_problem") # @time MathProgBase.writeproblem(SDP_problem, "/tmp/SDP_problem")
@ -78,7 +78,7 @@ function solve_SDP(SDP_problem, solver)
if solution_status != :Optimal if solution_status != :Optimal
warn("The solver did not solve the problem successfully!") warn("The solver did not solve the problem successfully!")
end end
@show solution_status info(logger, solution_status)
κ = JuMP.getvalue(JuMP.getvariable(SDP_problem, :κ)) κ = JuMP.getvalue(JuMP.getvariable(SDP_problem, :κ))
A = JuMP.getvalue(JuMP.getvariable(SDP_problem, :A)) A = JuMP.getvalue(JuMP.getvariable(SDP_problem, :A))