Support QR and LQ

Author: kshyatt

Project.toml

@@ -62,3 +62,6 @@ Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
 test = ["Aqua", "Combinatorics", "LinearAlgebra", "TensorOperations", "Test", "TestExtras", "ChainRulesCore", "ChainRulesTestUtils", "FiniteDifferences", "Zygote"]
+
+[sources]
+MatrixAlgebraKit = {url="https://github.com/QuantumKitHub/MatrixAlgebraKit.jl", rev="ksh/copyfix"}

src/TensorKit.jl

@@ -73,6 +73,8 @@ export mul!, lmul!, rmul!, adjoint!, pinv, axpy!, axpby!
 export leftorth, rightorth, leftnull, rightnull,
        leftorth!, rightorth!, leftnull!, rightnull!,
        left_polar, left_polar!, right_polar, right_polar!,
+       qr_full, qr_compact, qr_null, lq_full, lq_compact, lq_null,
+       qr_full!, qr_compact!, qr_null!, lq_full!, lq_compact!, lq_null!,
        tsvd!, tsvd, eigen, eigen!, eig, eig!, eigh, eigh!, exp, exp!,
        isposdef, isposdef!, ishermitian, isisometry, isunitary, sylvester, rank, cond
 export braid, braid!, permute, permute!, transpose, transpose!, twist, twist!, repartition,

src/tensors/factorizations/factorizations.jl

@@ -7,6 +7,10 @@ export eig, eig!, eigh, eigh!
 export tsvd, tsvd!, svdvals, svdvals!
 export leftorth, leftorth!, rightorth, rightorth!
 export leftnull, leftnull!, rightnull, rightnull!
+export qr_full, qr_compact, qr_null
+export qr_full!, qr_compact!, qr_null!
+export lq_full, lq_compact, lq_null
+export lq_full!, lq_compact!, lq_null!
 export copy_oftype, permutedcopy_oftype, one!
 export TruncationScheme, notrunc, truncbelow, truncerr, truncdim, truncspace, PolarViaSVD
 

test/factorizations.jl

@@ -29,6 +29,36 @@ for V in spacelist
                 # Test both a normal tensor and an adjoint one.
                 ts = (rand(T, W, W'), rand(T, W, W')', rand(T, V1, W'), rand(T, V1, W')')
                 @testset for t in ts
+                    @testset "qr_full" begin
+                        Q, R = @constinferred qr_full(t)
+                        @test isisometry(Q)
+                        @test Q * R ≈ t
+                    end
+                    @testset "qr_compact" begin
+                        Q, R = @constinferred qr_compact(t)
+                        @test isisometry(Q)
+                        @test Q * R ≈ t
+                    end
+                    @testset "qr_null" begin
+                        N = @constinferred qr_null(t)
+                        @test isisometry(N)
+                        @test norm(N' * t) < 100 * eps(norm(t))
+                    end
+                    @testset "lq_full" begin
+                        L, Q = @constinferred lq_full(t)
+                        @test isisometry(Q; side=:right)
+                        @test L * Q ≈ t
+                    end
+                    @testset "lq_compact" begin
+                        L, Q = @constinferred lq_compact(t)
+                        @test isisometry(Q; side=:right)
+                        @test L * Q ≈ t
+                    end
+                    @testset "lq_null" begin
+                        Nᴴ = @constinferred lq_null(t)
+                        @test isisometry(Nᴴ; side=:right)
+                        @test norm(t * Nᴴ') < 100 * eps(norm(t))
+                    end
                     @testset "leftorth with $alg" for alg in
                                                       (TensorKit.LAPACK_HouseholderQR(),
                                                        TensorKit.LAPACK_HouseholderQR(;