Update and use MatrixAlgebraKit.isisometry

Author: lkdvos

src/auxiliary/linalg.jl

@@ -84,8 +84,6 @@ end
 safesign(s::Real) = ifelse(s < zero(s), -one(s), +one(s))
 safesign(s::Complex) = ifelse(iszero(s), one(s), s / abs(s))
 
-isisometry(A::StridedMatrix; kwargs...) = isapprox(A' * A, LinearAlgebra.I, kwargs...)
-
 function leftorth!(A::StridedMatrix{<:BlasFloat}, alg::Union{QR,QRpos}, atol::Real)
     iszero(atol) || throw(ArgumentError("nonzero atol not supported by $alg"))
     m, n = size(A)

src/tensors/factorizations/factorizations.jl

@@ -36,7 +36,7 @@ import MatrixAlgebraKit: select_algorithm,
                          left_null_svd!, right_null_svd!,
                          left_orth!, right_orth!, left_null!, right_null!,
                          truncate!, findtruncated, findtruncated_sorted,
-                         diagview
+                         diagview, isisometry
 
 include("utility.jl")
 include("interface.jl")
@@ -176,10 +176,7 @@ end
 # TODO: tolerances are per-block, not global or weighted - does that matter?
 function isisometry(t::AbstractTensorMap; kwargs...)
     domain(t) ≾ codomain(t) || return false
-    for (_, b) in blocks(t)
-        MatrixAlgebra.isisometry(b; kwargs...) || return false
-    end
-    return true
+    return all(x -> isisometry(x[2]; kwargs...), blocks(t))
 end
 
 end

test/tensors.jl

@@ -365,9 +365,8 @@ for V in spacelist
             for T in (Float64, ComplexF64)
                 t1 = randisometry(T, W1, W2)
                 t2 = randisometry(T, W2 ← W2)
-                @test t1' * t1 ≈ one(t2)
-                @test t2' * t2 ≈ one(t2)
-                @test t2 * t2' ≈ one(t2)
+                @test isisometry(t1)
+                @test isunitary(t2)
                 P = t1 * t1'
                 @test P * P ≈ P
             end
@@ -447,21 +446,14 @@ for V in spacelist
                                                        TensorKit.Polar(), TensorKit.SVD(),
                                                        TensorKit.SDD())
                         Q, R = @constinferred leftorth(t, ((3, 4, 2), (1, 5)); alg=alg)
-                        QdQ = Q' * Q
-                        @test QdQ ≈ one(QdQ)
+                        @test isisometry(Q)
                         @test Q * R ≈ permute(t, ((3, 4, 2), (1, 5)))
-                        # removed since leftorth now merges legs!
-                        # if alg isa Polar
-                        #     @test isposdef(R)
-                        #     @test domain(R) == codomain(R) == space(t, 1)' ⊗ space(t, 5)'
-                        # end
                     end
                     @testset "leftnull with $alg" for alg in
                                                       (TensorKit.QR(), TensorKit.SVD(),
                                                        TensorKit.SDD())
                         N = @constinferred leftnull(t, ((3, 4, 2), (1, 5)); alg=alg)
-                        NdN = N' * N
-                        @test NdN ≈ one(NdN)
+                        @test isisometry(N)
                         @test norm(N' * permute(t, ((3, 4, 2), (1, 5)))) <
                               100 * eps(norm(t))
                     end
@@ -471,30 +463,21 @@ for V in spacelist
                                                         TensorKit.Polar(), TensorKit.SVD(),
                                                         TensorKit.SDD())
                         L, Q = @constinferred rightorth(t, ((3, 4), (2, 1, 5)); alg=alg)
-                        QQd = Q * Q'
-                        @test QQd ≈ one(QQd)
+                        @test isisometry(Q; kind=:right)
                         @test L * Q ≈ permute(t, ((3, 4), (2, 1, 5)))
-                        # removed since rightorth now merges legs!
-                        # if alg isa Polar
-                        #     @test isposdef(L)
-                        #     @test domain(L) == codomain(L) == space(t, 3) ⊗ space(t, 4)
-                        # end
                     end
                     @testset "rightnull with $alg" for alg in
                                                        (TensorKit.LQ(), TensorKit.SVD(),
                                                         TensorKit.SDD())
                         M = @constinferred rightnull(t, ((3, 4), (2, 1, 5)); alg=alg)
-                        MMd = M * M'
-                        @test MMd ≈ one(MMd)
+                        @test isisometry(M; kind=:right)
                         @test norm(permute(t, ((3, 4), (2, 1, 5))) * M') <
                               100 * eps(norm(t))
                     end
                     @testset "tsvd with $alg" for alg in (TensorKit.SVD(), TensorKit.SDD())
                         U, S, V = @constinferred tsvd(t, ((3, 4, 2), (1, 5)); alg=alg)
-                        UdU = U' * U
-                        @test UdU ≈ one(UdU)
-                        VVd = V * V'
-                        @test VVd ≈ one(VVd)
+                        @test isisometry(U)
+                        @test isisometry(V; kind=:right)
                         t2 = permute(t, ((3, 4, 2), (1, 5)))
                         @test U * S * V ≈ t2
 
@@ -537,8 +520,7 @@ for V in spacelist
                                                       (TensorKit.QR(), TensorKit.SVD(),
                                                        TensorKit.SDD())
                         N = @constinferred leftnull(t; alg=alg)
-                        @test N' * N ≈ id(domain(N))
-                        @test N * N' ≈ id(codomain(N))
+                        @test isunitary(N)
                     end
                     @testset "rightorth with $alg" for alg in
                                                        (TensorKit.RQ(), TensorKit.RQpos(),
@@ -553,8 +535,7 @@ for V in spacelist
                                                        (TensorKit.LQ(), TensorKit.SVD(),
                                                         TensorKit.SDD())
                         M = @constinferred rightnull(copy(t'); alg=alg)
-                        @test M * M' ≈ id(codomain(M))
-                        @test M' * M ≈ id(domain(M))
+                        @test isunitary(M)
                     end
                     @testset "tsvd with $alg" for alg in (TensorKit.SVD(), TensorKit.SDD())
                         U, S, V = @constinferred tsvd(t; alg=alg)
@@ -590,8 +571,7 @@ for V in spacelist
                     @test !isposdef(t2) # unlikely for non-hermitian map
                     t2 = (t2 + t2')
                     D, V = eigen(t2)
-                    VdV = V' * V
-                    @test VdV ≈ one(VdV)
+                    @test isisometry(V)
                     D̃, Ṽ = @constinferred eigh(t2)
                     @test D ≈ D̃
                     @test V ≈ Ṽ