Fix (l/r)mul! with Diagonal/Bidiagonal (#55052)

Author: jishnub

stdlib/LinearAlgebra/src/bidiag.jl

@@ -411,6 +411,32 @@ end
 /(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)
 
+# B .= D * B
+function lmul!(D::Diagonal, B::Bidiagonal)
+    _muldiag_size_check(D, B)
+    (; dv, ev) = B
+    isL = B.uplo == 'L'
+    dv[1] = D.diag[1] * dv[1]
+    for i in axes(ev,1)
+        ev[i] = D.diag[i + isL] * ev[i]
+        dv[i+1] = D.diag[i+1] * dv[i+1]
+    end
+    return B
+end
+
+# B .= B * D
+function rmul!(B::Bidiagonal, D::Diagonal)
+    _muldiag_size_check(B, D)
+    (; dv, ev) = B
+    isU = B.uplo == 'U'
+    dv[1] *= D.diag[1]
+    for i in axes(ev,1)
+        ev[i] *= D.diag[i + isU]
+        dv[i+1] *= D.diag[i+1]
+    end
+    return B
+end
+
 function ==(A::Bidiagonal, B::Bidiagonal)
     if A.uplo == B.uplo
         return A.dv == B.dv && A.ev == B.ev

stdlib/LinearAlgebra/src/diagonal.jl

@@ -294,8 +294,49 @@ end
 (*)(D::Diagonal, A::HermOrSym) =
     mul!(similar(A, promote_op(*, eltype(A), eltype(D.diag)), size(A)), D, A)
 
-rmul!(A::AbstractMatrix, D::Diagonal) = @inline mul!(A, A, D)
-lmul!(D::Diagonal, B::AbstractVecOrMat) = @inline mul!(B, D, B)
+function rmul!(A::AbstractMatrix, D::Diagonal)
+    _muldiag_size_check(A, D)
+    for I in CartesianIndices(A)
+        row, col = Tuple(I)
+        @inbounds A[row, col] *= D.diag[col]
+    end
+    return A
+end
+# T .= T * D
+function rmul!(T::Tridiagonal, D::Diagonal)
+    _muldiag_size_check(T, D)
+    (; dl, d, du) = T
+    d[1] *= D.diag[1]
+    for i in axes(dl,1)
+        dl[i] *= D.diag[i]
+        du[i] *= D.diag[i+1]
+        d[i+1] *= D.diag[i+1]
+    end
+    return T
+end
+
+function lmul!(D::Diagonal, B::AbstractVecOrMat)
+    _muldiag_size_check(D, B)
+    for I in CartesianIndices(B)
+        row = I[1]
+        @inbounds B[I] = D.diag[row] * B[I]
+    end
+    return B
+end
+
+# in-place multiplication with a diagonal
+# T .= D * T
+function lmul!(D::Diagonal, T::Tridiagonal)
+    _muldiag_size_check(D, T)
+    (; dl, d, du) = T
+    d[1] = D.diag[1] * d[1]
+    for i in axes(dl,1)
+        dl[i] = D.diag[i+1] * dl[i]
+        du[i] = D.diag[i] * du[i]
+        d[i+1] = D.diag[i+1] * d[i+1]
+    end
+    return T
+end
 
 function (*)(A::AdjOrTransAbsMat, D::Diagonal)
     Ac = copy_similar(A, promote_op(*, eltype(A), eltype(D.diag)))

stdlib/LinearAlgebra/test/bidiag.jl

@@ -827,4 +827,13 @@ end
     @test_throws "cannot set entry" B[1,2] = 4
 end
 
+@testset "rmul!/lmul! with banded matrices" begin
+    dv, ev = rand(4), rand(3)
+    for A in (Bidiagonal(dv, ev, :U), Bidiagonal(dv, ev, :L))
+        D = Diagonal(dv)
+        @test rmul!(copy(A), D) ≈ A * D
+        @test lmul!(D, copy(A)) ≈ D * A
+    end
+end
+
 end # module TestBidiagonal

stdlib/LinearAlgebra/test/diagonal.jl

@@ -1180,4 +1180,17 @@ end
     @test *(Diagonal(ones(n)), Diagonal(1:n), Diagonal(ones(n)), Diagonal(1:n)) isa Diagonal
 end
 
+@testset "rmul!/lmul! with banded matrices" begin
+    @testset "$(nameof(typeof(B)))" for B in (
+                            Bidiagonal(rand(4), rand(3), :L),
+                            Tridiagonal(rand(3), rand(4), rand(3))
+                    )
+        BA = Array(B)
+        D = Diagonal(rand(size(B,1)))
+        DA = Array(D)
+        @test rmul!(copy(B), D) ≈ B * D ≈ BA * DA
+        @test lmul!(D, copy(B)) ≈ D * B ≈ DA * BA
+    end
+end
+
 end # module TestDiagonal

stdlib/LinearAlgebra/test/tridiag.jl

@@ -802,4 +802,12 @@ end
     end
 end
 
+@testset "rmul!/lmul! with banded matrices" begin
+    dl, d, du = rand(3), rand(4), rand(3)
+    A = Tridiagonal(dl, d, du)
+    D = Diagonal(d)
+    @test rmul!(copy(A), D) ≈ A * D
+    @test lmul!(D, copy(A)) ≈ D * A
+end
+
 end # module TestTridiagonal