Specialize Diagonal * Matrix * Diagonal (#46400)

Author: chengchingwen

stdlib/LinearAlgebra/src/diagonal.jl

@@ -368,6 +368,12 @@ end
     return out
 end
 
+function (*)(Da::Diagonal, A::AbstractMatrix, Db::Diagonal)
+    _muldiag_size_check(Da, A)
+    _muldiag_size_check(A, Db)
+    return broadcast(*, Da.diag, A, permutedims(Db.diag))
+end
+
 # Get ambiguous method if try to unify AbstractVector/AbstractMatrix here using AbstractVecOrMat
 @inline mul!(out::AbstractVector, D::Diagonal, V::AbstractVector, alpha::Number, beta::Number) =
     _muldiag!(out, D, V, alpha, beta)

stdlib/LinearAlgebra/test/diagonal.jl

@@ -653,6 +653,16 @@ end
     @test D2 == D * D
 end
 
+@testset "multiplication of 2 Diagonal and a Matix (#46400)" begin
+    A = randn(10, 10)
+    D = Diagonal(randn(10))
+    D2 = Diagonal(randn(10))
+    @test D * A * D2 ≈ D * (A * D2)
+    @test D * A * D2 ≈ (D * A) * D2
+    @test_throws DimensionMismatch Diagonal(ones(9)) * A * D2
+    @test_throws DimensionMismatch D * A * Diagonal(ones(9))
+end
+
 @testset "multiplication of QR Q-factor and Diagonal (#16615 spot test)" begin
     D = Diagonal(randn(5))
     Q = qr(randn(5, 5)).Q