Use FastLapackInterface.jl?

[nathanaelbosch]

https://github.com/DynareJulia/FastLapackInterface.jl
We're already doing something similar in

ProbNumDiffEq.jl/src/fast_linalg.jl

Lines 57 to 91 in 70aee09

	"""
	getupperright!(A)
	Get the upper right part of a matrix `A` without allocating.
	This function is mostly there to make accessing `R` from a `QR` object more efficient, as
	`qr!(A).R` allocates since it does not use views. This function is not exported and is only
	ever used internally by `triangularize!`(@ref).
	"""
	function getupperright!(A)
	m, n = size(A)
	return UpperTriangular(triu!(A[1:min(m, n), 1:n]))
	end
	"""
	triangularize!(A; [cachemat])
	Compute `qr(A).R` in the most efficient and allocation-free way possible.
	The fallback implementation essentially computes `qr!(A).R`. But if `A` is of type
	`StridedMatrix{<:LinearAlgebra.BlasFloat}`, we can make things more efficient by calling
	LAPACK directly and using the preallocated cache `cachemat`.
	"""
	triangularize!(A; cachemat)
	function triangularize!(A; cachemat=nothing)
	QR = qr!(A)
	return getupperright!(getfield(QR, :factors))
	end
	function triangularize!(A::StridedMatrix{<:LinearAlgebra.BlasFloat}; cachemat)
	D = size(A, 2)
	BLOCKSIZE = 36
	R, _ = LinearAlgebra.LAPACK.geqrt!(A, @view cachemat[1:min(BLOCKSIZE, D), :])
	return getupperright!(R)
	end

but not quite. FastLapackInterface.jl might be the cleaner way to do this.