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60 lines
2.2 KiB
Julia
60 lines
2.2 KiB
Julia
@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 = "SL(3,Z)_orbit"
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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) < 5e-12
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@info "$NAME:\nDifference in l₁-norm between square and hpc sos decompositions:" norm(eoi-sos_sqr,1) norm(eoi-sos_hpc,1) norm(sos_sqr - sos_hpc, 1)
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#########################################################
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NAME = "SL(4,Z)_orbit"
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eoi, pm, Q = prepare(NAME, 1.3, 4*3*2)
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@time sos_sqr = PropertyT.compute_SOS_square(pm, Q)
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@time sos_hpc = PropertyT.compute_SOS(pm, Q)
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@test norm(sos_sqr - sos_hpc, 1) < 2e-10
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@info "$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 = "SAut(F3)_orbit"
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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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