Try to improve type stability with Householder

[lkdvos]

Here I standardized the Householder keyword arguments in an attempt to improve the type stability (again).

Apparently this just isn't enough, so I gave up again and just put the @assume_effects into place.
In general, I think this really is what we want, and the main point is that this should really only go wrong if default_algorithm isn't foldable, which is probably a fair thing to ask for.
I am also quite unhappy about this solution, and am very open to alternative suggestions, but I spent way too long on this already and am running out of ideas.

To give some insight into what I found:
The main thing seems to be that there is a maximal depth that the compiler will @inline or const-prop. For example, with some tinkering I actually got it to the point where select_algorithm(right_orth!, A, alg) is type stable, but select_algorithm(right_orth, A, alg) then wasn't, even though it is marked with inline annotations.
From this I concluded there is a maximal depth of logic we can achieve, and since the "orthnull" already is using up quite a bit of that I can't seem to get past it without a major rewrite

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.

Files with missing lines	Coverage Δ
ext/MatrixAlgebraKitGenericLinearAlgebraExt.jl	85.91% <100.00%> (ø)
src/algorithms.jl	88.73% <100.00%> (-1.27%)	⬇️
src/implementations/lq.jl	95.06% <100.00%> (+0.87%)	⬆️
src/implementations/qr.jl	95.08% <100.00%> (+0.94%)	⬆️
src/interface/decompositions.jl	70.37% <100.00%> (+6.37%)	⬆️
src/interface/lq.jl	62.50% <100.00%> (ø)
src/interface/orthnull.jl	70.58% <100.00%> (ø)
src/interface/qr.jl	62.50% <100.00%> (ø)

... and 3 files with indirect coverage changes

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[Jutho]

Any reason for not doing

Suggested change

	:(NamedTuple{$(Tuple(sort!(collect(K))))}(nt))
	:(NamedTuple{$(sort(K))}(nt))

[Jutho]

Also, don't know if this really requires a generated function:

julia> function _canonicalize_nt(x::NamedTuple{N}) where {N}
           return NamedTuple{sort(N)}(x)
       end
_canonicalize_nt (generic function with 1 method)

julia> _canonicalize_nt((; y=3, x=5))
(x = 5, y = 3)

julia> @code_warntype _canonicalize_nt((; y=3, x=5))
MethodInstance for _canonicalize_nt(::@NamedTuple{y::Int64, x::Int64})
  from _canonicalize_nt(x::NamedTuple{N}) where N @ Main REPL[10]:1
Static Parameters
  N = (:y, :x)
Arguments
  #self#::Core.Const(Main._canonicalize_nt)
  x::@NamedTuple{y::Int64, x::Int64}
Body::@NamedTuple{x::Int64, y::Int64}
1 ─ %1 = Main.NamedTuple::Core.Const(NamedTuple)
│   %2 = Main.sort::Core.Const(sort)
│   %3 = $(Expr(:static_parameter, 1))::Core.Const((:y, :x))
│   %4 = (%2)(%3)::Core.Const((:x, :y))
│   %5 = Core.apply_type(%1, %4)::Core.Const(NamedTuple{(:x, :y)})
│   %6 = (%5)(x)::@NamedTuple{x::Int64, y::Int64}
└──      return %6

[lkdvos]

I feel like I tried that but that didn't work, let me double check

[lkdvos]

Can confirm this doesn't work on Julia 1.10 😉

[Jutho]

I would like to see a final run with the non-generated function suggestion to canonicalize the NamedTuple field of Algorithm{Name}. Also, the qr and lq tests use the deprecated explicit LAPACK_HouseholderQR/LQ algorithms. I think these should probably have been fixed in the original PR, so maybe this can be included here?

[lkdvos]

@Jutho I think I have now more or less exhausted the ways of writing a generated function without using a generated function. The verdict is that on LTS sort(::Tuple{Vararg{Symbol}}) does not work, requiring Tuple(sort(collect(...))), which is then no longer type stable in the chain of default_algorithm functions, so I am just going to revert to the generated function since I do think this is a valid use-case.

[Jutho]

Ok, I quickly checked on LTS. That is indeed annoying. The one solution you did not think of is using TupleTools.sort 😄 . But I am fine with the current solution; maybe just add a comment that we can get rid of @generated when the LTS is at some point changed.