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split up fusiontree tests
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‎test/symmetries/doubletree.jl‎

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using Test, TestExtras
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using TensorKit
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import TensorKit as TK
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using Random: randperm
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using TensorOperations
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# TODO: remove this once type_repr works for all included types
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using TensorKitSectors
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@timedtestset "Fusion trees for $(TensorKit.type_repr(I))" verbose = true for I in (fast_tests ? fast_sectorlist : sectorlist)
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Istr = TensorKit.type_repr(I)
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@testset "Fusion tree $Istr: merging" begin
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N = 3
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out1 = random_fusion(I, Val(N))
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out2 = random_fusion(I, Val(N))
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in1 = rand(collect(⊗(out1...)))
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in2 = rand(collect(⊗(out2...)))
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tp = ⊗(in1, in2) # messy solution but it works
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while isempty(tp)
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out1 = random_fusion(I, Val(N))
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out2 = random_fusion(I, Val(N))
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in1 = rand(collect(⊗(out1...)))
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in2 = rand(collect(⊗(out2...)))
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tp = ⊗(in1, in2)
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end
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f1 = rand(collect(fusiontrees(out1, in1)))
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f2 = rand(collect(fusiontrees(out2, in2)))
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@constinferred TK.merge(f1, f2, first(in1 ⊗ in2), 1)
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if !(FusionStyle(I) isa GenericFusion)
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@constinferred TK.merge(f1, f2, first(in1 ⊗ in2), 1)
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@constinferred TK.merge(f1, f2, first(in1 ⊗ in2))
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end
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@test dim(in1) * dim(in2) ≈ sum(
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abs2(coeff) * dim(c) for c in in1 ⊗ in2
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for μ in 1:Nsymbol(in1, in2, c)
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for (f, coeff) in TK.merge(f1, f2, c, μ)
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)
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if BraidingStyle(I) isa HasBraiding
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for c in in1 ⊗ in2
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R = Rsymbol(in1, in2, c)
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for μ in 1:Nsymbol(in1, in2, c)
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trees1 = TK.merge(f1, f2, c, μ)
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# test merge and braid interplay
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trees2 = Dict{keytype(trees1), complex(valtype(trees1))}()
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trees3 = Dict{keytype(trees1), complex(valtype(trees1))}()
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for ν in 1:Nsymbol(in2, in1, c)
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for (t, coeff) in TK.merge(f2, f1, c, ν)
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trees2[t] = get(trees2, t, zero(valtype(trees2))) + coeff * R[μ, ν]
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end
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end
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perm = ((N .+ (1:N))..., (1:N)...)
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levels = ntuple(identity, 2 * N)
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for (t, coeff) in trees1
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for (t′, coeff′) in braid(t, levels, perm)
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trees3[t′] = get(trees3, t′, zero(valtype(trees3))) + coeff * coeff′
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end
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end
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for (t, coeff) in trees3
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coeff′ = get(trees2, t, zero(coeff))
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@test isapprox(coeff, coeff′; atol = 1.0e-12, rtol = 1.0e-12)
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end
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# test via conversion
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if (BraidingStyle(I) isa Bosonic) && hasfusiontensor(I)
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Af1 = convert(Array, f1)
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Af2 = convert(Array, f2)
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Af0 = convert(
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Array,
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FusionTree((f1.coupled, f2.coupled), c, (false, false), (), (μ,))
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)
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_Af = TensorOperations.tensorcontract(
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1:(N + 2), Af1, [1:N; -1], Af0, [-1; N + 1; N + 2]
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)
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Af = TensorOperations.tensorcontract(
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1:(2N + 1), Af2, [N .+ (1:N); -1], _Af, [1:N; -1; 2N + 1]
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)
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Af′ = zero(Af)
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for (f, coeff) in trees1
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Af′ .+= coeff .* convert(Array, f)
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end
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@test Af ≈ Af′
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end
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end
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end
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end
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end
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if I <: ProductSector
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N = 3
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else
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N = 4
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end
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if UnitStyle(I) isa SimpleUnit
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out = random_fusion(I, Val(N))
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numtrees = count(n -> true, fusiontrees((out..., map(dual, out)...)))
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while !(0 < numtrees < 100)
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out = random_fusion(I, Val(N))
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numtrees = count(n -> true, fusiontrees((out..., map(dual, out)...)))
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end
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incoming = rand(collect(⊗(out...)))
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f1 = rand(collect(fusiontrees(out, incoming, ntuple(n -> rand(Bool), N))))
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f2 = rand(collect(fusiontrees(out[randperm(N)], incoming, ntuple(n -> rand(Bool), N))))
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else
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out = random_fusion(I, Val(N))
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out2 = random_fusion(I, Val(N))
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tp = ⊗(out...)
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tp2 = ⊗(out2...)
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while isempty(intersect(tp, tp2)) # guarantee fusion to same coloring
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out2 = random_fusion(I, Val(N))
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tp2 = ⊗(out2...)
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end
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@test_throws ArgumentError fusiontrees((out..., map(dual, out)...))
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incoming = rand(collect(intersect(tp, tp2)))
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f1 = rand(collect(fusiontrees(out, incoming, ntuple(n -> rand(Bool), N))))
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f2 = rand(collect(fusiontrees(out2, incoming, ntuple(n -> rand(Bool), N)))) # no permuting
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end
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@testset "Double fusion tree $Istr: repartitioning" begin
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for n in 0:(2 * N)
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d = @constinferred TK.repartition(f1, f2, $n)
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@test dim(incoming) ≈
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sum(abs2(coef) * dim(f1.coupled) for ((f1, f2), coef) in d)
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d2 = Dict{typeof((f1, f2)), valtype(d)}()
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for ((f1′, f2′), coeff) in d
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for ((f1′′, f2′′), coeff2) in TK.repartition(f1′, f2′, N)
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d2[(f1′′, f2′′)] = get(d2, (f1′′, f2′′), zero(coeff)) + coeff2 * coeff
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end
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end
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for ((f1′, f2′), coeff2) in d2
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if f1 == f1′ && f2 == f2′
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@test coeff2 ≈ 1
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else
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@test isapprox(coeff2, 0; atol = 1.0e-12, rtol = 1.0e-12)
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end
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end
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if (BraidingStyle(I) isa Bosonic) && hasfusiontensor(I)
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Af1 = convert(Array, f1)
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Af2 = permutedims(convert(Array, f2), [N:-1:1; N + 1])
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sz1 = size(Af1)
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sz2 = size(Af2)
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d1 = prod(sz1[1:(end - 1)])
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d2 = prod(sz2[1:(end - 1)])
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dc = sz1[end]
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A = reshape(
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reshape(Af1, (d1, dc)) * reshape(Af2, (d2, dc))',
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(sz1[1:(end - 1)]..., sz2[1:(end - 1)]...)
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)
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A2 = zero(A)
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for ((f1′, f2′), coeff) in d
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Af1′ = convert(Array, f1′)
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Af2′ = permutedims(convert(Array, f2′), [(2N - n):-1:1; 2N - n + 1])
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sz1′ = size(Af1′)
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sz2′ = size(Af2′)
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d1′ = prod(sz1′[1:(end - 1)])
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d2′ = prod(sz2′[1:(end - 1)])
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dc′ = sz1′[end]
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A2 += coeff *
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reshape(
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reshape(Af1′, (d1′, dc′)) * reshape(Af2′, (d2′, dc′))',
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(sz1′[1:(end - 1)]..., sz2′[1:(end - 1)]...)
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)
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end
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@test A ≈ A2
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end
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end
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end
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@testset "Double fusion tree $Istr: permutation" begin
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if BraidingStyle(I) isa SymmetricBraiding
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for n in 0:(2N)
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p = (randperm(2 * N)...,)
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p1, p2 = p[1:n], p[(n + 1):(2N)]
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ip = invperm(p)
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ip1, ip2 = ip[1:N], ip[(N + 1):(2N)]
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d = @constinferred TK.permute(f1, f2, p1, p2)
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@test dim(incoming) ≈
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sum(abs2(coef) * dim(f1.coupled) for ((f1, f2), coef) in d)
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d2 = Dict{typeof((f1, f2)), valtype(d)}()
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for ((f1′, f2′), coeff) in d
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d′ = TK.permute(f1′, f2′, ip1, ip2)
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for ((f1′′, f2′′), coeff2) in d′
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d2[(f1′′, f2′′)] = get(d2, (f1′′, f2′′), zero(coeff)) +
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coeff2 * coeff
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end
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end
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for ((f1′, f2′), coeff2) in d2
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if f1 == f1′ && f2 == f2′
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@test coeff2 ≈ 1
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else
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@test abs(coeff2) < 1.0e-12
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end
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end
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if (BraidingStyle(I) isa Bosonic) && hasfusiontensor(I)
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A = convert(Array, (f1, f2))
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Ap = permutedims(A, (p1..., p2...))
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A2 = zero(Ap)
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for ((f1′, f2′), coeff) in d
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A2 .+= coeff .* convert(Array, (f1′, f2′))
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end
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@test Ap ≈ A2
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end
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end
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end
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end
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@testset "Double fusion tree $Istr: transposition" begin
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for n in 0:(2N)
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i0 = rand(1:(2N))
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p = mod1.(i0 .+ (1:(2N)), 2N)
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ip = mod1.(-i0 .+ (1:(2N)), 2N)
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p′ = tuple(getindex.(Ref(vcat(1:N, (2N):-1:(N + 1))), p)...)
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p1, p2 = p′[1:n], p′[(2N):-1:(n + 1)]
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ip′ = tuple(getindex.(Ref(vcat(1:n, (2N):-1:(n + 1))), ip)...)
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ip1, ip2 = ip′[1:N], ip′[(2N):-1:(N + 1)]
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d = @constinferred transpose(f1, f2, p1, p2)
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@test dim(incoming) ≈
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sum(abs2(coef) * dim(f1.coupled) for ((f1, f2), coef) in d)
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d2 = Dict{typeof((f1, f2)), valtype(d)}()
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for ((f1′, f2′), coeff) in d
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d′ = transpose(f1′, f2′, ip1, ip2)
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for ((f1′′, f2′′), coeff2) in d′
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d2[(f1′′, f2′′)] = get(d2, (f1′′, f2′′), zero(coeff)) + coeff2 * coeff
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end
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end
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for ((f1′, f2′), coeff2) in d2
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if f1 == f1′ && f2 == f2′
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@test coeff2 ≈ 1
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else
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@test abs(coeff2) < 1.0e-12
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end
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end
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if BraidingStyle(I) isa Bosonic
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d3 = permute(f1, f2, p1, p2)
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for (f1′, f2′) in union(keys(d), keys(d3))
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coeff1 = get(d, (f1′, f2′), zero(valtype(d)))
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coeff3 = get(d3, (f1′, f2′), zero(valtype(d3)))
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@test isapprox(coeff1, coeff3; atol = 1.0e-12)
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end
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end
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if (BraidingStyle(I) isa Bosonic) && hasfusiontensor(I)
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Af1 = convert(Array, f1)
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Af2 = convert(Array, f2)
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sz1 = size(Af1)
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sz2 = size(Af2)
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d1 = prod(sz1[1:(end - 1)])
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d2 = prod(sz2[1:(end - 1)])
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dc = sz1[end]
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A = reshape(
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reshape(Af1, (d1, dc)) * reshape(Af2, (d2, dc))',
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(sz1[1:(end - 1)]..., sz2[1:(end - 1)]...)
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)
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Ap = permutedims(A, (p1..., p2...))
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A2 = zero(Ap)
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for ((f1′, f2′), coeff) in d
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Af1′ = convert(Array, f1′)
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Af2′ = convert(Array, f2′)
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sz1′ = size(Af1′)
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sz2′ = size(Af2′)
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d1′ = prod(sz1′[1:(end - 1)])
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d2′ = prod(sz2′[1:(end - 1)])
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dc′ = sz1′[end]
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A2 += coeff * reshape(
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reshape(Af1′, (d1′, dc′)) *
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reshape(Af2′, (d2′, dc′))',
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(sz1′[1:(end - 1)]..., sz2′[1:(end - 1)]...)
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)
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end
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@test Ap ≈ A2
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end
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end
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end
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@testset "Double fusion tree $Istr: planar trace" begin
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d1 = transpose(f1, f1, (N + 1, 1:N..., ((2N):-1:(N + 3))...), (N + 2,))
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f1front, = TK.split(f1, N - 1)
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T = sectorscalartype(I)
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d2 = Dict{typeof((f1front, f1front)), T}()
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for ((f1′, f2′), coeff′) in d1
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for ((f1′′, f2′′), coeff′′) in
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TK.planar_trace(
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f1′, f2′, (2:N...,), (1, ((2N):-1:(N + 3))...), (N + 1,),
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(N + 2,)
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)
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coeff = coeff′ * coeff′′
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d2[(f1′′, f2′′)] = get(d2, (f1′′, f2′′), zero(coeff)) + coeff
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end
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end
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for ((f1_, f2_), coeff) in d2
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if (f1_, f2_) == (f1front, f1front)
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@test coeff ≈ dim(f1.coupled) / dim(f1front.coupled)
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else
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@test abs(coeff) < 1.0e-12
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end
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end
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end
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TK.empty_globalcaches!()
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end

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