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split up factorization tests
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‎test/factorizations/eig.jl‎

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using Test, TestExtras
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using TensorKit
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using LinearAlgebra: LinearAlgebra
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using MatrixAlgebraKit: diagview
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spacelist = if fast_tests
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(Vtr, Vℤ₃, VSU₂)
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elseif get(ENV, "CI", "false") == "true"
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println("Detected running on CI")
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if Sys.iswindows()
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(Vtr, Vℤ₃, VU₁, VfU₁, VCU₁, VSU₂, VIB_diag)
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elseif Sys.isapple()
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(Vtr, Vℤ₃, VfU₁, VfSU₂, VIB_M)
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else
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(Vtr, VU₁, VCU₁, VSU₂, VfSU₂, VIB_diag, VIB_M)
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end
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else
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(Vtr, Vℤ₃, VU₁, VfU₁, VCU₁, VSU₂, VfSU₂, VIB_diag, VIB_M)
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end
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eltypes = (Float32, ComplexF64)
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for V in spacelist
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I = sectortype(first(V))
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Istr = TensorKit.type_repr(I)
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println("---------------------------------------")
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println("Factorizations with symmetry: $Istr")
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println("---------------------------------------")
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@timedtestset "Factorizations with symmetry: $Istr" verbose = true begin
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V1, V2, V3, V4, V5 = V
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W = V1 ⊗ V2
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@assert !isempty(blocksectors(W))
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@assert !isempty(intersect(blocksectors(V4), blocksectors(W)))
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@testset "Eigenvalue decomposition" begin
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for T in eltypes,
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t in (
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rand(T, V1, V1), rand(T, W, W), rand(T, W, W)',
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DiagonalTensorMap(rand(T, reduceddim(V1)), V1),
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)
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d, v = @constinferred eig_full(t)
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@test t * v ≈ v * d
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d′ = @constinferred eig_vals(t)
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@test d′ ≈ diagview(d)
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@test d′ isa TensorKit.SectorVector
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d2 = @constinferred DiagonalTensorMap(d′)
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@test d2 ≈ d
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vdv = project_hermitian!(v' * v)
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@test @constinferred isposdef(vdv)
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t isa DiagonalTensorMap || @test !isposdef(t) # unlikely for non-hermitian map
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nvals = round(Int, dim(domain(t)) / 2)
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d, v = @constinferred eig_trunc(t; trunc = truncrank(nvals))
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@test t * v ≈ v * d
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test_dim_isapprox(domain(d), nvals)
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t2 = @constinferred project_hermitian(t)
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D, V = eigen(t2)
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@test isisometric(V)
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D̃, Ṽ = @constinferred eigh_full(t2)
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@test D ≈ D̃
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@test V ≈ Ṽ
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λ = minimum(real, diagview(D))
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@test cond(Ṽ) ≈ one(real(T))
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@test isposdef(t2) == isposdef(λ)
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@test isposdef(t2 - λ * one(t2) + 0.1 * one(t2))
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@test !isposdef(t2 - λ * one(t2) - 0.1 * one(t2))
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d, v = @constinferred eigh_full(t2)
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@test t2 * v ≈ v * d
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@test isunitary(v)
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d′ = @constinferred eigh_vals(t2)
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@test d′ ≈ diagview(d)
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@test d′ isa TensorKit.SectorVector
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λ = minimum(real, diagview(d))
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@test cond(v) ≈ one(real(T))
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@test isposdef(t2) == isposdef(λ)
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@test isposdef(t2 - λ * one(t) + 0.1 * one(t2))
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@test !isposdef(t2 - λ * one(t) - 0.1 * one(t2))
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d, v = @constinferred eigh_trunc(t2; trunc = truncrank(nvals))
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@test t2 * v ≈ v * d
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test_dim_isapprox(domain(d), nvals)
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end
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end
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end
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end

‎test/factorizations/ortho.jl‎

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using Test, TestExtras
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using TensorKit
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using LinearAlgebra: LinearAlgebra
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using MatrixAlgebraKit: diagview
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spacelist = if fast_tests
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(Vtr, Vℤ₃, VSU₂)
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elseif get(ENV, "CI", "false") == "true"
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println("Detected running on CI")
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if Sys.iswindows()
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(Vtr, Vℤ₃, VU₁, VfU₁, VCU₁, VSU₂, VIB_diag)
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elseif Sys.isapple()
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(Vtr, Vℤ₃, VfU₁, VfSU₂, VIB_M)
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else
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(Vtr, VU₁, VCU₁, VSU₂, VfSU₂, VIB_diag, VIB_M)
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end
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else
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(Vtr, Vℤ₃, VU₁, VfU₁, VCU₁, VSU₂, VfSU₂, VIB_diag, VIB_M)
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end
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eltypes = (Float32, ComplexF64)
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for V in spacelist
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I = sectortype(first(V))
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Istr = TensorKit.type_repr(I)
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println("---------------------------------------")
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println("Factorizations with symmetry: $Istr")
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println("---------------------------------------")
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@timedtestset "Factorizations with symmetry: $Istr" verbose = true begin
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V1, V2, V3, V4, V5 = V
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W = V1 ⊗ V2
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@assert !isempty(blocksectors(W))
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@assert !isempty(intersect(blocksectors(V4), blocksectors(W)))
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@testset "QR decomposition" begin
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for T in eltypes,
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t in (
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rand(T, W, W), rand(T, W, W)', rand(T, W, V4), rand(T, V4, W)',
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DiagonalTensorMap(rand(T, reduceddim(V1)), V1),
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)
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Q, R = @constinferred qr_full(t)
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@test Q * R ≈ t
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@test isunitary(Q)
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Q, R = @constinferred qr_compact(t)
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@test Q * R ≈ t
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@test isisometric(Q)
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Q, R = @constinferred left_orth(t)
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@test Q * R ≈ t
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@test isisometric(Q)
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N = @constinferred qr_null(t)
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@test isisometric(N)
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@test norm(N' * t) ≈ 0 atol = 100 * eps(norm(t))
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N = @constinferred left_null(t)
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@test isisometric(N)
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@test norm(N' * t) ≈ 0 atol = 100 * eps(norm(t))
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end
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# empty tensor
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for T in eltypes
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t = rand(T, V1 ⊗ V2, zerospace(V1))
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Q, R = @constinferred qr_full(t)
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@test Q * R ≈ t
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@test isunitary(Q)
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@test dim(R) == dim(t) == 0
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Q, R = @constinferred qr_compact(t)
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@test Q * R ≈ t
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@test isisometric(Q)
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@test dim(Q) == dim(R) == dim(t)
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Q, R = @constinferred left_orth(t)
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@test Q * R ≈ t
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@test isisometric(Q)
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@test dim(Q) == dim(R) == dim(t)
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N = @constinferred qr_null(t)
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@test isunitary(N)
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@test norm(N' * t) ≈ 0 atol = 100 * eps(norm(t))
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end
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end
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@testset "LQ decomposition" begin
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for T in eltypes,
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t in (
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rand(T, W, W), rand(T, W, W)', rand(T, W, V4), rand(T, V4, W)',
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DiagonalTensorMap(rand(T, reduceddim(V1)), V1),
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)
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L, Q = @constinferred lq_full(t)
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@test L * Q ≈ t
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@test isunitary(Q)
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L, Q = @constinferred lq_compact(t)
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@test L * Q ≈ t
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@test isisometric(Q; side = :right)
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L, Q = @constinferred right_orth(t)
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@test L * Q ≈ t
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@test isisometric(Q; side = :right)
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Nᴴ = @constinferred lq_null(t)
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@test isisometric(Nᴴ; side = :right)
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@test norm(t * Nᴴ') ≈ 0 atol = 100 * eps(norm(t))
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end
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for T in eltypes
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# empty tensor
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t = rand(T, zerospace(V1), V1 ⊗ V2)
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L, Q = @constinferred lq_full(t)
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@test L * Q ≈ t
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@test isunitary(Q)
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@test dim(L) == dim(t) == 0
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L, Q = @constinferred lq_compact(t)
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@test L * Q ≈ t
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@test isisometric(Q; side = :right)
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@test dim(Q) == dim(L) == dim(t)
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L, Q = @constinferred right_orth(t)
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@test L * Q ≈ t
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@test isisometric(Q; side = :right)
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@test dim(Q) == dim(L) == dim(t)
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Nᴴ = @constinferred lq_null(t)
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@test isunitary(Nᴴ)
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@test norm(t * Nᴴ') ≈ 0 atol = 100 * eps(norm(t))
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end
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end
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end
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end

‎test/factorizations/projections.jl‎

Lines changed: 131 additions & 0 deletions
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using Test, TestExtras
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using TensorKit
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using LinearAlgebra: LinearAlgebra
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using MatrixAlgebraKit: diagview
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6+
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spacelist = if fast_tests
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(Vtr, Vℤ₃, VSU₂)
9+
elseif get(ENV, "CI", "false") == "true"
10+
println("Detected running on CI")
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if Sys.iswindows()
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(Vtr, Vℤ₃, VU₁, VfU₁, VCU₁, VSU₂, VIB_diag)
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elseif Sys.isapple()
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(Vtr, Vℤ₃, VfU₁, VfSU₂, VIB_M)
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else
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(Vtr, VU₁, VCU₁, VSU₂, VfSU₂, VIB_diag, VIB_M)
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end
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else
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(Vtr, Vℤ₃, VU₁, VfU₁, VCU₁, VSU₂, VfSU₂, VIB_diag, VIB_M)
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end
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eltypes = (Float32, ComplexF64)
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for V in spacelist
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I = sectortype(first(V))
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Istr = TensorKit.type_repr(I)
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println("---------------------------------------")
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println("Factorizations with symmetry: $Istr")
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println("---------------------------------------")
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@timedtestset "Factorizations with symmetry: $Istr" verbose = true begin
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V1, V2, V3, V4, V5 = V
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W = V1 ⊗ V2
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@assert !isempty(blocksectors(W))
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@assert !isempty(intersect(blocksectors(V4), blocksectors(W)))
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@testset "Condition number and rank" begin
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for T in eltypes,
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t in (
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rand(T, W, W), rand(T, W, W)',
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rand(T, W, V4), rand(T, V4, W),
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rand(T, W, V4)', rand(T, V4, W)',
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DiagonalTensorMap(rand(T, reduceddim(V1)), V1),
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)
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d1, d2 = dim(codomain(t)), dim(domain(t))
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r = rank(t)
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@test r == min(d1, d2)
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@test typeof(r) == typeof(d1)
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M = left_null(t)
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@test @constinferred(rank(M)) + r ≈ d1
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Mᴴ = right_null(t)
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@test rank(Mᴴ) + r ≈ d2
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end
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for T in eltypes
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u = unitary(T, V1 ⊗ V2, V1 ⊗ V2)
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@test @constinferred(cond(u)) ≈ one(real(T))
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@test @constinferred(rank(u)) == dim(V1 ⊗ V2)
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t = rand(T, zerospace(V1), W)
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@test rank(t) == 0
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t2 = rand(T, zerospace(V1) * zerospace(V2), zerospace(V1) * zerospace(V2))
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@test rank(t2) == 0
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@test cond(t2) == 0.0
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end
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for T in eltypes, t in (rand(T, W, W), rand(T, W, W)')
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project_hermitian!(t)
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vals = @constinferred LinearAlgebra.eigvals(t)
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λmax = maximum(s -> maximum(abs, s), values(vals))
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λmin = minimum(s -> minimum(abs, s), values(vals))
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@test cond(t) ≈ λmax / λmin
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end
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end
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@testset "Hermitian projections" begin
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for T in eltypes,
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t in (
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rand(T, V1, V1), rand(T, W, W), rand(T, W, W)',
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DiagonalTensorMap(rand(T, reduceddim(V1)), V1),
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)
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normalize!(t)
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noisefactor = eps(real(T))^(3 / 4)
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th = (t + t') / 2
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ta = (t - t') / 2
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tc = copy(t)
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th′ = @constinferred project_hermitian(t)
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@test ishermitian(th′)
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@test th′ ≈ th
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@test t == tc
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th_approx = th + noisefactor * ta
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@test !ishermitian(th_approx) || (T <: Real && t isa DiagonalTensorMap)
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@test ishermitian(th_approx; atol = 10 * noisefactor)
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ta′ = project_antihermitian(t)
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@test isantihermitian(ta′)
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@test ta′ ≈ ta
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@test t == tc
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ta_approx = ta + noisefactor * th
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@test !isantihermitian(ta_approx)
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@test isantihermitian(ta_approx; atol = 10 * noisefactor) || (T <: Real && t isa DiagonalTensorMap)
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end
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end
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@testset "Isometric projections" begin
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for T in eltypes,
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t in (
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randn(T, W, W), randn(T, W, W)',
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randn(T, W, V4), randn(T, V4, W)',
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)
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t2 = project_isometric(t)
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@test isisometric(t2)
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t3 = project_isometric(t2)
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@test t3 ≈ t2 # stability of the projection
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@test t2 * (t2' * t) ≈ t
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tc = similar(t)
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t3 = @constinferred project_isometric!(copy!(tc, t), t2)
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@test t3 === t2
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@test isisometric(t2)
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# test that t2 is closer to A then any other isometry
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for k in 1:10
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δt = randn!(similar(t))
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t3 = project_isometric(t + δt / 100)
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@test norm(t - t3) > norm(t - t2)
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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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