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test the correctness of hpc sos computation
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@ -37,14 +37,18 @@ function compute_SOS(RG::GroupRing, Q::AbstractMatrix{<:Real})
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return GroupRingElem(result, RG)
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end
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function compute_SOS_square(RG::GroupRing, Q::AbstractMatrix{<:Real})
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result = zeros(eltype(Q), maximum(RG.pm));
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function compute_SOS_square(pm::AbstractMatrix{<:Integer}, Q::AbstractMatrix{<:Real})
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result = zeros(eltype(Q), maximum(pm));
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for i in 1:size(Q,2)
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GroupRings.fmac!(result, view(Q,:,i), view(Q,:,i), RG.pm)
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GroupRings.fmac!(result, view(Q,:,i), view(Q,:,i), pm)
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end
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return GroupRingElem(result, RG)
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return result
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end
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function compute_SOS_square(RG::GroupRing, Q::AbstractMatrix{<:Real})
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return GroupRingElem(compute_SOS_square(RG.pm, Q), RG)
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end
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function augIdproj(Q::AbstractMatrix{T}) where {T<:Real}
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61
test/SOS_correctness.jl
Normal file
61
test/SOS_correctness.jl
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@ -0,0 +1,61 @@
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using PropertyT.GroupRings
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@testset "Correctness of HPC SOS computation" begin
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function prepare(G_name, λ, S_size)
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pm = load("$G_name/delta.jld", "pm")
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P = load("$G_name/$λ/solution.jld", "P")
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@time Q = real(sqrt(P))
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Δ_coeff = SparseVector(maximum(pm), collect(1:1+S_size), [S_size; ((-1.0) for i in 1:S_size)...])
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Δ²_coeff = GroupRings.GRmul!(spzeros(length(Δ_coeff)), Δ_coeff, Δ_coeff, pm)
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eoi = Δ²_coeff - λ*Δ_coeff
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Q = PropertyT.augIdproj(Q)
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return eoi, pm, Q
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end
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#########################################################
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NAME = "SL(3,Z)"
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eoi, pm, Q = prepare(NAME, 0.1, 3*2*2)
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@time sos_sqr = PropertyT.compute_SOS_square(pm, Q)
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@time sos_hpc = PropertyT.compute_SOS(pm, Q)
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@test norm(sos_sqr - sos_hpc, 1) < 3e-12
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@info "$NAME:\nDifference in l₁-norm between square and hpc sos decompositions:" norm(eoi-sos_sqr,1) norm(eoi-sos_hpc,1) norm(sos_sqr - sos_hpc, 1)
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#########################################################
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NAME = "oSL(3,Z)"
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eoi, pm, Q = prepare(NAME, 0.27, 3*2*2)
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@time sos_sqr = PropertyT.compute_SOS_square(pm, Q)
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@time sos_hpc = PropertyT.compute_SOS(pm, Q)
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@test norm(sos_sqr - sos_hpc, 1) < 3e-12
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@info "$NAME:\nDifference in l₁-norm between square and hpc sos decompositions:" norm(eoi-sos_sqr,1) norm(eoi-sos_hpc,1) norm(sos_sqr - sos_hpc, 1)
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#########################################################
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NAME = "oSL(4,Z)"
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eoi, pm, Q = prepare(NAME, 1.3, 4*3*2)
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@time sos_sqr = PropertyT.compute_SOS_square(pm, Q)
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@time sos_hpc = PropertyT.compute_SOS(pm, Q)
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@test norm(sos_sqr - sos_hpc, 1) < 2e-10
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@info "$NAME:\nDifference in l₁-norm between square and hpc sos decompositions:" norm(eoi-sos_sqr,1) norm(eoi-sos_hpc,1) norm(sos_sqr - sos_hpc, 1)
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#########################################################
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NAME = "oSAut(F3)"
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eoi, pm, Q = prepare(NAME, 0.15, 4*3*2*2)
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@time sos_sqr = PropertyT.compute_SOS_square(pm, Q)
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@time sos_hpc = PropertyT.compute_SOS(pm, Q)
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@test norm(sos_sqr - sos_hpc, 1) < 6e-11
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@info "$NAME:\nDifference in l₁-norm between square and hpc sos decompositions:" norm(eoi-sos_sqr,1) norm(eoi-sos_hpc,1) norm(sos_sqr - sos_hpc, 1)
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end
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@ -15,10 +15,11 @@ function Groups.gens(M::MatSpace)
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return S
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end
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solver(iters; accel=1) =
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with_optimizer(SCS.Optimizer,
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solver(iters; accel=1) =
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with_optimizer(SCS.Optimizer,
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linear_solver=SCS.Direct, max_iters=iters,
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acceleration_lookback=accel, eps=1e-10, warm_start=true)
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include("1703.09680.jl")
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include("1712.07167.jl")
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include("SOS_correctness.jl")
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