JuliaLang / julia / #37939

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Commit Message

Reroute` (Upper/Lower)Triangular * Diagonal` through `__muldiag` (#55984)

Currently, `::Diagonal * ::AbstractMatrix` calls the method
`LinearAlgebra.__muldiag!` in general that scales the rows, and
similarly for the diagonal on the right. The implementation of
`__muldiag` was duplicating the logic in `LinearAlgebra.modify!` and the
methods for `MulAddMul`. This PR replaces the various branches with
calls to `modify!` instead. I've also extracted the multiplication logic
into its own function `__muldiag_nonzeroalpha!` so that this may be
specialized for matrix types, such as triangular ones.

Secondly, `::Diagonal * ::UpperTriangular` (and similarly, other
triangular matrices) was specialized to forward the multiplication to
the parent of the triangular. For strided matrices, however, it makes
more sense to use the structure and scale only the filled half of the
matrix. Firstly, this improves performance, and secondly, this avoids
errors in case the parent isn't fully initialized corresponding to the
structural zero elements.

Performance improvement:
```julia
julia> D = Diagonal(1:400);

julia> U = UpperTriangular(zeros(size(D)));

julia> @btime $D * $U;
  314.944 μs (3 allocations: 1.22 MiB) # v"1.12.0-DEV.1288"
  195.960 μs (3 allocations: 1.22 MiB) # This PR
```
Fix:
```julia
julia> M = Matrix{BigFloat}(undef, 2, 2);

julia> M[1,1] = M[2,2] = M[1,2] = 3;

julia> U = UpperTriangular(M)
2×2 UpperTriangular{BigFloat, Matrix{BigFloat}}:
 3.0  3.0
  ⋅   3.0

julia> D = Diagonal(1:2);

julia> U * D # works after this PR
2×2 UpperTriangular{BigFloat, Matrix{BigFloat}}:
 3.0  6.0
  ⋅   6.0
```

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