Add \ for Sym/Tri/Bi/Diagonal and support non-commutative numbers (#3…

…9701)

Co-authored-by: Daniel Karrasch <daniel.karrasch@posteo.de>

stdlib/LinearAlgebra/src/bidiag.jl

@@ -371,8 +371,9 @@ end
 
 -(A::Bidiagonal)=Bidiagonal(-A.dv,-A.ev,A.uplo)
 *(A::Bidiagonal, B::Number) = Bidiagonal(A.dv*B, A.ev*B, A.uplo)
-*(B::Number, A::Bidiagonal) = A*B
+*(B::Number, A::Bidiagonal) = Bidiagonal(B*A.dv, B*A.ev, A.uplo)
 /(A::Bidiagonal, B::Number) = Bidiagonal(A.dv/B, A.ev/B, A.uplo)
+\(B::Number, A::Bidiagonal) = Bidiagonal(B\A.dv, B\A.ev, A.uplo)
 
 function ==(A::Bidiagonal, B::Bidiagonal)
     if A.uplo == B.uplo

stdlib/LinearAlgebra/src/diagonal.jl

@@ -174,6 +174,7 @@ end
 (*)(x::Number, D::Diagonal) = Diagonal(x * D.diag)
 (*)(D::Diagonal, x::Number) = Diagonal(D.diag * x)
 (/)(D::Diagonal, x::Number) = Diagonal(D.diag / x)
+(\)(x::Number, D::Diagonal) = Diagonal(x \ D.diag)
 
 function (*)(Da::Diagonal, Db::Diagonal)
     nDa, mDb = size(Da, 2), size(Db, 1)

stdlib/LinearAlgebra/src/tridiag.jl

@@ -206,8 +206,9 @@ end
 -(A::SymTridiagonal, B::SymTridiagonal) = SymTridiagonal(A.dv-B.dv, A.ev-B.ev)
 -(A::SymTridiagonal) = SymTridiagonal(-A.dv, -A.ev)
 *(A::SymTridiagonal, B::Number) = SymTridiagonal(A.dv*B, A.ev*B)
-*(B::Number, A::SymTridiagonal) = A*B
+*(B::Number, A::SymTridiagonal) = SymTridiagonal(B*A.dv, B*A.ev)
 /(A::SymTridiagonal, B::Number) = SymTridiagonal(A.dv/B, A.ev/B)
+\(B::Number, A::SymTridiagonal) = SymTridiagonal(B\A.dv, B\A.ev)
 ==(A::SymTridiagonal, B::SymTridiagonal) = (A.dv==B.dv) && (A.ev==B.ev)
 
 @inline mul!(A::StridedVecOrMat, B::SymTridiagonal, C::StridedVecOrMat,
@@ -733,8 +734,9 @@ end
 +(A::Tridiagonal, B::Tridiagonal) = Tridiagonal(A.dl+B.dl, A.d+B.d, A.du+B.du)
 -(A::Tridiagonal, B::Tridiagonal) = Tridiagonal(A.dl-B.dl, A.d-B.d, A.du-B.du)
 *(A::Tridiagonal, B::Number) = Tridiagonal(A.dl*B, A.d*B, A.du*B)
-*(B::Number, A::Tridiagonal) = A*B
+*(B::Number, A::Tridiagonal) = Tridiagonal(B*A.dl, B*A.d, B*A.du)
 /(A::Tridiagonal, B::Number) = Tridiagonal(A.dl/B, A.d/B, A.du/B)
+\(B::Number, A::Tridiagonal) = Tridiagonal(B\A.dl, B\A.d, B\A.du)
 
 ==(A::Tridiagonal, B::Tridiagonal) = (A.dl==B.dl) && (A.d==B.d) && (A.du==B.du)
 ==(A::Tridiagonal, B::SymTridiagonal) = (A.dl==A.du==B.ev) && (A.d==B.dv)

stdlib/LinearAlgebra/test/bidiag.jl

@@ -5,6 +5,11 @@ module TestBidiagonal
 using Test, LinearAlgebra, SparseArrays, Random
 using LinearAlgebra: BlasReal, BlasFloat
 
+const BASE_TEST_PATH = joinpath(Sys.BINDIR, "..", "share", "julia", "test")
+
+isdefined(Main, :Quaternions) || @eval Main include(joinpath($(BASE_TEST_PATH), "testhelpers", "Quaternions.jl"))
+using .Main.Quaternions
+
 include("testutils.jl") # test_approx_eq_modphase
 
 n = 10 #Size of test matrix
@@ -635,4 +640,13 @@ end
     @test ubd .* 3 == ubd
 end
 
+@testset "non-commutative algebra (#39701)" begin
+    A = Bidiagonal(Quaternion.(randn(5), randn(5), randn(5), randn(5)), Quaternion.(randn(4), randn(4), randn(4), randn(4)), :U)
+    c = Quaternion(1,2,3,4)
+    @test A * c ≈ Matrix(A) * c
+    @test A / c ≈ Matrix(A) / c
+    @test c * A ≈ c * Matrix(A)
+    @test c \ A ≈ c \ Matrix(A)
+end
+
 end # module TestBidiagonal

stdlib/LinearAlgebra/test/tridiag.jl

@@ -4,6 +4,11 @@ module TestTridiagonal
 
 using Test, LinearAlgebra, SparseArrays, Random
 
+const BASE_TEST_PATH = joinpath(Sys.BINDIR, "..", "share", "julia", "test")
+
+isdefined(Main, :Quaternions) || @eval Main include(joinpath($(BASE_TEST_PATH), "testhelpers", "Quaternions.jl"))
+using .Main.Quaternions
+
 include("testutils.jl") # test_approx_eq_modphase
 
 #Test equivalence of eigenvectors/singular vectors taking into account possible phase (sign) differences
@@ -587,4 +592,15 @@ end
     @test F.values ≈ F2.values
 end
 
+@testset "non-commutative algebra (#39701)" begin
+    for A in (SymTridiagonal(Quaternion.(randn(5), randn(5), randn(5), randn(5)), Quaternion.(randn(4), randn(4), randn(4), randn(4))),
+              Tridiagonal(Quaternion.(randn(4), randn(4), randn(4), randn(4)), Quaternion.(randn(5), randn(5), randn(5), randn(5)), Quaternion.(randn(4), randn(4), randn(4), randn(4))))
+        c = Quaternion(1,2,3,4)
+        @test A * c ≈ Matrix(A) * c
+        @test A / c ≈ Matrix(A) / c
+        @test c * A ≈ c * Matrix(A)
+        @test c \ A ≈ c \ Matrix(A)
+    end
+end
+
 end # module TestTridiagonal