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add diagonal tensor tests
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‎test/test_A4.jl‎

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@@ -2,6 +2,7 @@ using MultiTensorKit
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using TensorKitSectors, TensorKit
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using Test, TestExtras
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using Random
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using LinearAlgebra: LinearAlgebra
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const MTK = MultiTensorKit
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const TK = TensorKit
@@ -600,6 +601,237 @@ println("---------------------------------------")
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end
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end
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println("-------------------------------------------")
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println("| Multifusion diagonal tensor tests |")
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println("-------------------------------------------")
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V = Vect[I](values(I)[k] => 1 for k in 1:length(values(I)))
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@timedtestset "DiagonalTensor" begin
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@timedtestset "Basic properties and algebra" begin
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for T in (Float32, Float64, ComplexF32, ComplexF64, BigFloat)
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# constructors
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t = @constinferred DiagonalTensorMap{T}(undef, V)
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t = @constinferred DiagonalTensorMap(rand(T, reduceddim(V)), V)
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t2 = @constinferred DiagonalTensorMap{T}(undef, space(t))
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@test space(t2) == space(t)
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@test_throws ArgumentError DiagonalTensorMap{T}(undef, V^2 ← V)
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t2 = @constinferred DiagonalTensorMap{T}(undef, domain(t))
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@test space(t2) == space(t)
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@test_throws ArgumentError DiagonalTensorMap{T}(undef, V^2)
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# properties
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@test @constinferred(hash(t)) == hash(deepcopy(t))
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@test scalartype(t) == T
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@test codomain(t) == ProductSpace(V)
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@test domain(t) == ProductSpace(V)
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@test space(t) == (V ← V)
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@test space(t') == (V ← V)
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@test dim(t) == dim(space(t))
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# blocks
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bs = @constinferred blocks(t)
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(c, b1), state = @constinferred Nothing iterate(bs)
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@test c == first(blocksectors(V ← V))
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next = @constinferred Nothing iterate(bs, state)
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b2 = @constinferred block(t, first(blocksectors(t)))
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@test b1 == b2
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@test eltype(bs) === Pair{typeof(c),typeof(b1)}
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@test typeof(b1) === TK.blocktype(t)
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# basic linear algebra
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@test isa(@constinferred(norm(t)), real(T))
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@test norm(t)^2 ≈ dot(t, t)
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α = rand(T)
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@test norm(α * t) ≈ abs(α) * norm(t)
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@test norm(t + t, 2) ≈ 2 * norm(t, 2)
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@test norm(t + t, 1) ≈ 2 * norm(t, 1)
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@test norm(t + t, Inf) ≈ 2 * norm(t, Inf)
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p = 3 * rand(Float64)
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@test norm(t + t, p) ≈ 2 * norm(t, p)
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@test norm(t) ≈ norm(t')
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@test t == @constinferred(TensorMap(t))
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@test norm(t + TensorMap(t)) ≈ 2 * norm(t)
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@test norm(zerovector!(t)) == 0
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@test norm(one!(t)) ≈ sqrt(dim(V))
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@test one!(t) == id(V)
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@test norm(one!(t) - id(V)) == 0
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t1 = DiagonalTensorMap(rand(T, reduceddim(V)), V)
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t2 = DiagonalTensorMap(rand(T, reduceddim(V)), V)
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t3 = DiagonalTensorMap(rand(T, reduceddim(V)), V)
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α = rand(T)
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β = rand(T)
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@test @constinferred(dot(t1, t2)) ≈ conj(dot(t2, t1))
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@test dot(t2, t1) ≈ conj(dot(t2', t1'))
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@test dot(t3, α * t1 + β * t2) ≈ α * dot(t3, t1) + β * dot(t3, t2)
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end
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end
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@timedtestset "Basic linear algebra: test via conversion" begin
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for T in (Float32, ComplexF64)
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t1 = DiagonalTensorMap(rand(T, reduceddim(V)), V)
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t2 = DiagonalTensorMap(rand(T, reduceddim(V)), V)
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@test norm(t1, 2) ≈ norm(convert(TensorMap, t1), 2)
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@test dot(t2, t1) ≈ dot(convert(TensorMap, t2), convert(TensorMap, t1))
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α = rand(T)
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@test convert(TensorMap, α * t1) ≈ α * convert(TensorMap, t1)
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@test convert(TensorMap, t1') ≈ convert(TensorMap, t1)'
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@test convert(TensorMap, t1 + t2) ≈
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convert(TensorMap, t1) + convert(TensorMap, t2)
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end
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end
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@timedtestset "Real and imaginary parts" begin
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for T in (Float64, ComplexF64, ComplexF32)
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t = DiagonalTensorMap(rand(T, reduceddim(V)), V)
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tr = @constinferred real(t)
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@test scalartype(tr) <: Real
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@test real(convert(TensorMap, t)) == convert(TensorMap, tr)
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ti = @constinferred imag(t)
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@test scalartype(ti) <: Real
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@test imag(convert(TensorMap, t)) == convert(TensorMap, ti)
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tc = @inferred complex(t)
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@test scalartype(tc) <: Complex
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@test complex(convert(TensorMap, t)) == convert(TensorMap, tc)
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tc2 = @inferred complex(tr, ti)
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@test tc2 ≈ tc
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end
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end
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@timedtestset "Tensor conversion" begin
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t = @constinferred DiagonalTensorMap(undef, V)
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rand!(t.data)
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# element type conversion
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tc = complex(t)
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@test convert(typeof(tc), t) == tc
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@test typeof(convert(typeof(tc), t)) == typeof(tc)
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# to and from generic TensorMap
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td = DiagonalTensorMap(TensorMap(t))
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@test t == td
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@test typeof(td) == typeof(t)
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end
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@timedtestset "Trace, Multiplication and inverse" begin
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t1 = DiagonalTensorMap(rand(Float64, reduceddim(V)), V)
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t2 = DiagonalTensorMap(rand(ComplexF64, reduceddim(V)), V)
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@test tr(TensorMap(t1)) == @constinferred tr(t1)
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@test tr(TensorMap(t2)) == @constinferred tr(t2)
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@test TensorMap(@constinferred t1 * t2) ≈ TensorMap(t1) * TensorMap(t2)
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@test TensorMap(@constinferred t1 \ t2) ≈ TensorMap(t1) \ TensorMap(t2)
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@test TensorMap(@constinferred t1 / t2) ≈ TensorMap(t1) / TensorMap(t2)
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@test TensorMap(@constinferred inv(t1)) ≈ inv(TensorMap(t1))
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@test TensorMap(@constinferred pinv(t1)) ≈ pinv(TensorMap(t1))
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@test all(Base.Fix2(isa, DiagonalTensorMap),
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(t1 * t2, t1 \ t2, t1 / t2, inv(t1), pinv(t1)))
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# no V * V' * V ← V or V^2 ← V tests due to Nsymbol erroring where fusion is forbidden
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end
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@timedtestset "Tensor contraction " for i in 1:r
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W = Vect[I]((i, i, label) => 2 for label in 1:MTK._numlabels(I, i, i))
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d = DiagonalTensorMap(rand(ComplexF64, reduceddim(W)), W)
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t = TensorMap(d)
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A = randn(ComplexF64, W ⊗ W' ⊗ W, W)
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B = randn(ComplexF64, W ⊗ W' ⊗ W, W ⊗ W') # empty for modules so untested
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@planar E1[-1 -2 -3; -4 -5] := B[-1 -2 -3; 1 -5] * d[1; -4]
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@planar E2[-1 -2 -3; -4 -5] := B[-1 -2 -3; 1 -5] * t[1; -4]
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@test E1 ≈ E2
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@planar E1[-1 -2 -3; -4 -5] = B[-1 -2 -3; -4 1] * d'[-5; 1]
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@planar E2[-1 -2 -3; -4 -5] = B[-1 -2 -3; -4 1] * t'[-5; 1]
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@test E1 ≈ E2
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@planar E1[-1 -2 -3; -4 -5] = B[1 -2 -3; -4 -5] * d[-1; 1]
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@planar E2[-1 -2 -3; -4 -5] = B[1 -2 -3; -4 -5] * t[-1; 1]
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@test E1 ≈ E2
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@planar E1[-1 -2 -3; -4 -5] = B[-1 1 -3; -4 -5] * d[1; -2]
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@planar E2[-1 -2 -3; -4 -5] = B[-1 1 -3; -4 -5] * t[1; -2]
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@test E1 ≈ E2
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@planar E1[-1 -2 -3; -4 -5] = B[-1 -2 1; -4 -5] * d'[-3; 1]
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@planar E2[-1 -2 -3; -4 -5] = B[-1 -2 1; -4 -5] * t'[-3; 1]
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@test E1 ≈ E2
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end
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@timedtestset "Factorization" begin
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for T in (Float32, ComplexF64)
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t = DiagonalTensorMap(rand(T, reduceddim(V)), V)
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@testset "eig" begin
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D, W = @constinferred eig(t)
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@test t * W ≈ W * D
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t2 = t + t'
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D2, V2 = @constinferred eigh(t2)
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VdV2 = V2' * V2
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@test VdV2 ≈ one(VdV2)
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@test t2 * V2 ≈ V2 * D2
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@test rank(D) ≈ rank(t)
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@test cond(D) ≈ cond(t)
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@test all(((s, t),) -> isapprox(s, t),
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zip(values(LinearAlgebra.eigvals(D)),
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values(LinearAlgebra.eigvals(t))))
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end
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@testset "leftorth with $alg" for alg in (TK.QR(), TK.QL())
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Q, R = @constinferred leftorth(t; alg=alg)
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QdQ = Q' * Q
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@test QdQ ≈ one(QdQ)
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@test Q * R ≈ t
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if alg isa Polar
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@test isposdef(R)
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end
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end
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@testset "rightorth with $alg" for alg in (TK.RQ(), TK.LQ())
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L, Q = @constinferred rightorth(t; alg=alg)
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QQd = Q * Q'
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@test QQd ≈ one(QQd)
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@test L * Q ≈ t
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if alg isa Polar
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@test isposdef(L)
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end
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end
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@testset "tsvd with $alg" for alg in (TK.SVD(), TK.SDD())
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U, S, Vᴴ = @constinferred tsvd(t; alg=alg)
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UdU = U' * U
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@test UdU ≈ one(UdU)
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VdV = Vᴴ * Vᴴ'
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@test VdV ≈ one(VdV)
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@test U * S * Vᴴ ≈ t
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@test rank(S) ≈ rank(t)
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@test cond(S) ≈ cond(t)
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@test all(((s, t),) -> isapprox(s, t),
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zip(values(LinearAlgebra.svdvals(S)),
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values(LinearAlgebra.svdvals(t))))
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end
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end
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end
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@timedtestset "Tensor functions" begin
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for T in (Float64, ComplexF64)
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d = DiagonalTensorMap(rand(T, reduceddim(V)), V)
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# rand is important for positive numbers in the real case, for log and sqrt
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t = TensorMap(d)
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@test @constinferred exp(d) ≈ exp(t)
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@test @constinferred log(d) ≈ log(t)
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@test @constinferred sqrt(d) ≈ sqrt(t)
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@test @constinferred sin(d) ≈ sin(t)
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@test @constinferred cos(d) ≈ cos(t)
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@test @constinferred tan(d) ≈ tan(t)
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@test @constinferred cot(d) ≈ cot(t)
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@test @constinferred sinh(d) ≈ sinh(t)
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@test @constinferred cosh(d) ≈ cosh(t)
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@test @constinferred tanh(d) ≈ tanh(t)
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@test @constinferred coth(d) ≈ coth(t)
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@test @constinferred asin(d) ≈ asin(t)
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@test @constinferred acos(d) ≈ acos(t)
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@test @constinferred atan(d) ≈ atan(t)
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@test @constinferred acot(d) ≈ acot(t)
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@test @constinferred asinh(d) ≈ asinh(t)
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@test @constinferred acosh(one(d) + d) ≈ acosh(one(t) + t)
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@test @constinferred atanh(d) ≈ atanh(t)
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@test @constinferred acoth(one(t) + d) ≈ acoth(one(d) + t)
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end
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end
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end
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@testset "$Istr ($i, $j) left and right units" for i in 1:r, j in 1:r
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Cij_obs = I.(i, j, MTK._get_dual_cache(I)[2][i, j])
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