Specialize Diagonal * Adjoint (#1207)

This reinstates slightly altered versions of the methods that were
removed in JuliaLang/julia#52389. Sort of fixes
#1205, although this doesn't recover the full performance. However, this
version is more general, and works with the example presented in
JuliaLang/julia#52389. There's still a
performance regression, but the full performance may only be obtained
for mutable matrices, and we may not assume mutability in general.

Performance:
v1.10:

```julia
julia> n = 100
100

julia> A = adjoint(sparse(Float64, I, n, n));

julia> B = Diagonal(ones(n));

julia> @Btime $A * $B;
  837.119 ns (5 allocations: 2.59 KiB)
```

This PR
```julia
julia> @Btime $A * $B;
  1.106 μs (15 allocations: 5.56 KiB)
```
We need double the allocations here compared to earlier, as we firstly
materialize `D' * A'`, and then we again copy the adjoint of this
result. I wonder if this may be reduced.

---------

Co-authored-by: Daniel Karrasch <[email protected]>

Author: jishnub

src/adjtrans.jl

@@ -319,8 +319,8 @@ const AdjointAbsVec{T} = Adjoint{T,<:AbstractVector}
 const AdjointAbsMat{T} = Adjoint{T,<:AbstractMatrix}
 const TransposeAbsVec{T} = Transpose{T,<:AbstractVector}
 const TransposeAbsMat{T} = Transpose{T,<:AbstractMatrix}
-const AdjOrTransAbsVec{T} = AdjOrTrans{T,<:AbstractVector}
-const AdjOrTransAbsMat{T} = AdjOrTrans{T,<:AbstractMatrix}
+const AdjOrTransAbsVec{T,V<:AbstractVector} = AdjOrTrans{T,V}
+const AdjOrTransAbsMat{T,M<:AbstractMatrix} = AdjOrTrans{T,M}
 
 # for internal use below
 wrapperop(_) = identity

src/diagonal.jl

@@ -332,6 +332,28 @@ function (*)(D::Diagonal, V::AbstractVector)
     return D.diag .* V
 end
 
+function _diag_adj_mul(A::AdjOrTransAbsMat, D::Diagonal)
+    adj = wrapperop(A)
+    copy(adj(adj(D) * adj(A)))
+end
+function _diag_adj_mul(A::AdjOrTransAbsMat{<:Number, <:StridedMatrix}, D::Diagonal{<:Number})
+    @invoke *(A::AbstractMatrix, D::AbstractMatrix)
+end
+function _diag_adj_mul(D::Diagonal, A::AdjOrTransAbsMat)
+    adj = wrapperop(A)
+    copy(adj(adj(A) * adj(D)))
+end
+function _diag_adj_mul(D::Diagonal{<:Number}, A::AdjOrTransAbsMat{<:Number, <:StridedMatrix})
+    @invoke *(D::AbstractMatrix, A::AbstractMatrix)
+end
+
+function (*)(A::AdjOrTransAbsMat, D::Diagonal)
+    _diag_adj_mul(A, D)
+end
+function (*)(D::Diagonal, A::AdjOrTransAbsMat)
+    _diag_adj_mul(D, A)
+end
+
 function rmul!(A::AbstractMatrix, D::Diagonal)
     matmul_size_check(size(A), size(D))
     for I in CartesianIndices(A)