minor fixes in multiplication with Diagonals (#31443)

* minor fixes in multiplication with Diagonals

* correct rmul!(A,D), revert changes in AdjTrans(x)*D

* [r/l]mul!: replace conj by adjoint, add transpose

* add tests

* fix typo

* relax some tests, added more tests

* simplify tests, strict equality

(cherry picked from commit a93185f)

Author: dkarrasch

stdlib/LinearAlgebra/src/diagonal.jl

@@ -172,7 +172,7 @@ end
 
 function rmul!(A::AbstractMatrix, D::Diagonal)
     @assert !has_offset_axes(A)
-    A .= A .* transpose(D.diag)
+    A .= A .* permutedims(D.diag)
     return A
 end
 
@@ -260,20 +260,20 @@ lmul!(A::Diagonal, B::Diagonal) = Diagonal(B.diag .= A.diag .* B.diag)
 
 function lmul!(adjA::Adjoint{<:Any,<:Diagonal}, B::AbstractMatrix)
     A = adjA.parent
-    return lmul!(conj(A.diag), B)
+    return lmul!(adjoint(A), B)
 end
 function lmul!(transA::Transpose{<:Any,<:Diagonal}, B::AbstractMatrix)
     A = transA.parent
-    return lmul!(A.diag, B)
+    return lmul!(transpose(A), B)
 end
 
 function rmul!(A::AbstractMatrix, adjB::Adjoint{<:Any,<:Diagonal})
     B = adjB.parent
-    return rmul!(A, conj(B.diag))
+    return rmul!(A, adjoint(B))
 end
 function rmul!(A::AbstractMatrix, transB::Transpose{<:Any,<:Diagonal})
     B = transB.parent
-    return rmul!(A, B.diag)
+    return rmul!(A, transpose(B))
 end
 
 # Get ambiguous method if try to unify AbstractVector/AbstractMatrix here using AbstractVecOrMat
@@ -552,10 +552,9 @@ end
 *(x::Adjoint{<:Any,<:AbstractVector}, D::Diagonal) = Adjoint(map((t,s) -> t'*s, D.diag, parent(x)))
 *(x::Adjoint{<:Any,<:AbstractVector}, D::Diagonal, y::AbstractVector) =
     mapreduce(t -> t[1]*t[2]*t[3], +, zip(x, D.diag, y))
-*(x::Transpose{<:Any,<:AbstractVector}, D::Diagonal) = Transpose(map(*, D.diag, parent(x)))
+*(x::Transpose{<:Any,<:AbstractVector}, D::Diagonal) = Transpose(map((t,s) -> transpose(t)*s, D.diag, parent(x)))
 *(x::Transpose{<:Any,<:AbstractVector}, D::Diagonal, y::AbstractVector) =
     mapreduce(t -> t[1]*t[2]*t[3], +, zip(x, D.diag, y))
-# TODO: these methods will yield row matrices, rather than adjoint/transpose vectors
 
 function cholesky!(A::Diagonal, ::Val{false} = Val(false); check::Bool = true)
     info = 0

stdlib/LinearAlgebra/test/diagonal.jl

@@ -461,10 +461,20 @@ end
         fullBB = copyto!(Matrix{Matrix{T}}(undef, 2, 2), BB)
         for (transform1, transform2) in ((identity,  identity),
                 (identity,  adjoint  ), (adjoint,   identity ), (adjoint,   adjoint  ),
-                (identity,  transpose), (transpose, identity ), (transpose, transpose) )
+                (identity,  transpose), (transpose, identity ), (transpose, transpose),
+                (identity,  Adjoint  ), (Adjoint,   identity ), (Adjoint,   Adjoint  ),
+                (identity,  Transpose), (Transpose, identity ), (Transpose, Transpose))
             @test *(transform1(D), transform2(B))::typeof(D) ≈ *(transform1(Matrix(D)), transform2(Matrix(B))) atol=2 * eps()
             @test *(transform1(DD), transform2(BB))::typeof(DD) == *(transform1(fullDD), transform2(fullBB))
         end
+        M = randn(T, 5, 5)
+        MM = [randn(T, 2, 2) for _ in 1:2, _ in 1:2]
+        for transform in (identity, adjoint, transpose, Adjoint, Transpose)
+            @test lmul!(transform(D), copy(M)) == *(transform(Matrix(D)), M)
+            @test rmul!(copy(M), transform(D)) == *(M, transform(Matrix(D)))
+            @test lmul!(transform(DD), copy(MM)) == *(transform(fullDD), MM)
+            @test rmul!(copy(MM), transform(DD)) == *(MM, transform(fullDD))
+        end
     end
 end
 
@@ -474,10 +484,16 @@ end
 end
 
 @testset "Multiplication with Adjoint and Transpose vectors (#26863)" begin
-    x = rand(5)
-    D = Diagonal(rand(5))
-    @test x'*D*x == (x'*D)*x == (x'*Array(D))*x
-    @test Transpose(x)*D*x == (Transpose(x)*D)*x == (Transpose(x)*Array(D))*x
+    x = collect(1:2)
+    xt = transpose(x)
+    A = reshape([[1 2; 3 4], zeros(Int,2,2), zeros(Int, 2, 2), [5 6; 7 8]], 2, 2)
+    D = Diagonal(A)
+    @test x'*D == x'*A == copy(x')*D == copy(x')*A
+    @test xt*D == xt*A == copy(xt)*D == copy(xt)*A
+    y = [x, x]
+    yt = transpose(y)
+    @test y'*D*y == (y'*D)*y == (y'*A)*y
+    @test yt*D*y == (yt*D)*y == (yt*A)*y
 end
 
 @testset "Triangular division by Diagonal #27989" begin